2 Mark Question

Question 12 Marks

The hypotenuse of a triangle is 2.5cm. If one of the sides is 1.5cm. find the length of the other side.

Answer

Let the hypotenuse be" c " and the other two sides be" b " and " c".
Using the Pythagoras theorem, we can say that:
$c^2=a^2+b^2$
$2.52=1.52+b^2$
$b^2=6.25-2.25=4$
$c=2 cm$
Hence, the length of the other side is 2 cm .

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Question 22 Marks

Verity that the following number represent Pythagorean triplet:
$15,36,39$

Answer

We will check for a Pythagorean triplet by checking if the square of the largest side is equal to the sum of the squares of the other two sides.
$39^2=1521$
$15^2+36^2$
$=225+1296=1521$
$15^2+36^2=39^2$
Yes, they represent a Pythagorean triplet.

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Question 32 Marks

Is it possible to have a triangle, in which.
Two of the angles are obtuse?

Answer

Give reasons in support of your answer in.
No, because as we know that the sum of all three angles of a triangle is always 180°. If there are two obtuse angles, then their sum will be more than 180°, which is not possible in case of a triangle.

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Question 42 Marks

Explain the following term:
Equilateral triangle.

Answer

An equilateral triangle is a triangle in which all three sides are equal. Equilateral triangle.

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Question 52 Marks

If the sides of a triangle are 3cm, 4cm and 6cm long, determine whether the triangle is right-angled triangle.

Answer

In the given triangle, the largest side is 6cm.
We know that in a right angled triangle, the sum of the squares of the smaller sides should be equal to the square of the largest side.
Therefore,
$3^2+42=9+16=25$
But,
$6^2$ = $36$ $3^2$ + $4^2$ not equal to $6^2$
Hence, the given triangle is not a right angled triangle.

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Question 62 Marks

In right $\triangle \text{ABC},$ the lengths of the legs are given. Find the length of the hypotenuse.
$a=8 cm, b=15 cm$

Answer

According to the Pythagoras theorem,
$(Hypotenuse)^2=(Base)^2+(Height)^2$
$c^2=a^2+b^2$
$c^2=8^2+15^2$
$c^2=64+225=289$
$c=17 cm$

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Question 72 Marks

In the following, there are three positive numbers. State if these number could possibly be the lengths of the sides of a triangle:
2, 10.15

Answer

No, these numbers cannot be the lengths of the sides of a triangle because the sum of any two sides of a triangle is always greater than the third side, which is not true in this case.

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Question 82 Marks

The two legs of a right triangle are equal and the square of the hypotenuse is 50. Find the length of each leg.

Answer

Let the length of each leg of the given triangle be $x$ units.
Using the Pythagoras theorem, we get:
$x^2+x^2=(\text { Hypotenuse })^2$
$x^2+x^2=50$
$2 x^2=50$
$x^2=25$
$x=5$
Hence, we can say that the length of each leg is 5 units.

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Question 92 Marks

In the following, there are three positive numbers. State if these number could possibly be the lengths of the sides of a triangle:
3, 4, 5

Answer

Yes, these numbers can be the lengths of the sides of a triangle because the sum of any two sides of triangle is always greater than the third side. Here, 3 + 4 > 5, 3 + 5 > 4, 4 + 5 > 3

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Question 102 Marks

In the following, there are three positive numbers. State if these number could possibly be the lengths of the sides of a triangle:
5, 7, 9

Answer

Yes, these numbers can be the lengths of the sides of a triangle because the sum of any two sides of a triangle is always greater than the third side. Here, 5 + 7 > 9, 5 + 9 > 7, 9 + 7 > 5

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Question 112 Marks

Distinguish between a triangle and its triangular region.

Answer

A triangle is a plane figure formed by three non-parallel line segments, whereas, its triangular region includes the interior of the triangle along with the triangle itself.

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Question 122 Marks

Explain the following term:
Triangle.

Answer

A triangle is a plane figure formed by three non-parallel line segments.

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Question 132 Marks

Verity that the following number represent Pythagorean triplet:
$12,35,37$

Answer

We will check for a Pythagorean triplet by checking if the square of the largest side is equal to the sum of the squares of the other two sides.
$372=1369 \\
122+352 \\
=144+1225=1369 \\
122+352=37^2$
Yes, they represent a Pythagorean triplet.

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Question 142 Marks

In the following, there are three positive numbers. State if these number could possibly be the lengths of the sides of a triangle:
2, 5, 7

Answer

No, these numbers cannot be the lengths of the sides of a triangle because the sum of any two sides of a triangle is always greater than the third side, which is not true in this case. Here, 2 + 5 = 7

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Question 152 Marks

Is it possible to have a triangle, in which.
Two of the angles are acute?

Answer

Give reasons in support of your answer in.
Yes, in right triangles and acute triangles, it is possible to have two acute angles.

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Question 162 Marks

The sides of certain triangles are given below. Determine which of them are right triangles.
$a=9 cm, b=16 cm$ and $c=18 cm$

Answer

We know that in a right angled triangle, the square of the largest side is equal to the sum of the squares of the smaller sides.
Here, the larger side is c , which is 18 cm .
$c^2=324$
We have:
$a^2+b^2$
$=9^2+16^2$
$=81+256$
$=337$ not equal to $c^2$
Thus, the given triangle is not a right triangle.

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Question 172 Marks

Explain the following term:
Isosceles triangle.

Answer

An isosceles triangle is a triangle in which two sides are equal. Isosceles triangle.

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Question 182 Marks

The sides of certain triangles are given below. Determine which of them are right triangles.
$a=7 cm, b=24 cm \text { and } c=25 cm$

Answer

We know that in a right angled triangle, the square of the largest side is equal to the sum of the squares of the smaller sides. Here, the larger side is c , which is 25 cm .
$c^2=625$
We have:
$a^2+b^2$
$=7^2+24^2$
$=49+576$
$=625=c^2$
Thus, the given triangle is a right triangle.

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Question 192 Marks

Verity that the following number represent Pythagorean triplet:
$7,24,25$

Answer

We will check for a Pythagorean triplet by checking if the square of the largest side is equal to the sum of the squares of the other two sides.
$25^2=625$
$7^2+24^2$
$=49+576=625$
$7^2+24^2=25^2$
Yes, they represent a Pythagorean triplet.

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Question 202 Marks

Explain the following term:
Scalene triangle.

Answer

A scalene triangle is a triangle in which no two sides are equal.

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Question 212 Marks

In the following, there are three positive numbers. State if these number could possibly be the lengths of the sides of a triangle:
5, 8, 20

Answer

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Question 222 Marks

What is the difference between a triangle and triangular region?

Answer

Plane of figure formed by three non-parallel line segments is called a triangle where as triangular region is the interior of triangle ABC together with the triangle ABC itself is called the triangular region ABC.

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Question 232 Marks

$\angle\text{CBX}$ is an exterior angle of $\triangle \text{ABC}$ at B. Name.

The interior adjacent angle.
The interior opposite angles to exterior $\angle\text{CBX}$

Also, name the interior opposite angles to an exterior angle at A.

Answer

The interior angle ajacent to exterior $\angle \text{CBX}$ is $\angle \text{ABC}$
The interior angles opposite to exterior $\angle \text{CBX}$ are $\angle \text{BAC}$ and $\angle \text{ACB}$

Also, the interior angles opposite to exterior $\angle \text{BAY}$ are $\angle \text{ABC}$ and $\angle \text{ACB}$

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Question 242 Marks

Explain the following term:
Scalene triangle.

Answer

A scalene triangle is a triangle in which no two sides are equal.

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Question 252 Marks

D is a point on side BC of a $\triangle \text{CAD}$ is joined. Name all the triangles that you can observe in the figure. How many are they?

Answer

We can observe the following three triangles in the given figure:

$\triangle \text{ABC}$
$\triangle \text{ACD}$
$\triangle \text{ADB}$

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Question 262 Marks

Explain the following term:
Acute triangle.

Answer

An acute triangle is a triangle in which all the angles are acute (less than 90°).

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Question 272 Marks

Is it possible to have a triangle, in which.
Two of the angles are right?

Answer

Give reasons in support of your answer in.
No, because if there are two right angles in a triangle, then the third angle of the triangle must be zero, which is not possible.

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Question 282 Marks

In right $\triangle \text{ABC},$ the lengths of the legs are given. Find the length of the hypotenuse.
a = 3cm, b = 4cm

Answer

According to the Pythagoras theorem,
$(\text { Hypotenuse })^2=(\text { Base })^2+(\text { Height })^2$
$c^2=a^2+b^2$
$c^2=3^2+4^2$
$c^2=9+16=25$
$c=5 cm$

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Question 292 Marks

In right $\triangle ABC$, the lengths of the legs are given. Find the length of the hypotenuse.
$a=2 cm, b=1.5 cm$

Answer

According to the Pythagoras theorem,
$(\text { Hypotenuse })^2=(\text { Base })^2+(\text { Height })^2$
$c^2=a^2+b^2$
$c^2=2^2+1.5^2$
$c^2=4+2.25=6.25$
$c=2.5 cm$

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Question 302 Marks

Explain the following term:
Right triangle.

Answer

A right angled triangle is a triangle in which one angle is right angled, i.e. 90°.

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Question 312 Marks

In right $\triangle \text{ABC},$ the lengths of the legs are given. Find the length of the hypotenuse.
$a=6 cm, b=8 cm$

Answer

According to the Pythagoras theorem,
$(\text { Hypotenuse })^2=(\text { Base })^2+(\text { Height })^2$
$c^2=a^2+b^2$
$c^2=6^2+8^2$
$c^2=36+64=100$
$c=10 cm$

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Question 322 Marks

Explain the following term:
Exterior of a triangle.

Answer

The exterior of a triangle is made up of all such points that are not enclosed within the triangle.

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Question 332 Marks

Explain the following term:
Parts or elements of a triangle.

Answer

The three sides and the three angles of a triangle are together known as the parts or elements of that triangle.

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Question 342 Marks

Explain the following term:
Interior of a triangle.

Answer

The interior of a triangle is made up of all such points that are enclosed with in the triangle.

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Question 352 Marks

A, B, C and D are four points, and no three points are collinear. AC and BD intersed at O. There are eight triangles that you can observe. Name all the triangles.

Answer

$\triangle\text{ABC}$
$\triangle\text{ABD}$
$\triangle\text{ABO}$
$\triangle\text{BCD}$
$\triangle\text{DCO}$
$\triangle\text{AOD}$
$\triangle\text{ACD}$
$\triangle\text{BCD}$

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Question 362 Marks

Verity that the following number represent Pythagorean triplet:
$27,36,45$

Answer

We will check for a Pythagorean triplet by checking if the square of the largest side is equal to the sum of the squares of the other two sides.
$45^2=2025$
$27^2+36^2$
$=729+1296=2025$
$27^2+36^2=45^2$
Yes, they represent a Pythagorean triplet.

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Question 372 Marks

Explain the following term:
Obtuse triangle.

Answer

An obtuse triangle is a triangle in which one angle is obtuse (more than 90°).

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Question 382 Marks

In $\triangle \text{ABC}, \angle \text{A}=100^\circ,\angle \text{B}=30^\circ, \angle \text{C}=50^\circ.$ Name the smallest and the largest sides of the triangle.

Answer

Because the smallest side is always opposite to the smallest angle, which in this case is 30º, it is AC. Also, because the largest side is always opposite to the largest angle, which in this case is 100º, it is BC.

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Maths 2 Mark Question

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