3 Mark Question

Question 13 Marks

The sides of a rectangle are in the ratio 4 : 5 and its perimeter is 180cm. Find its sides.

Answer

Let the length be 4x cm and the breadth be 5x cm.
Perimeter of the rectangle =180cm.
Perimeter of the rectangle = 2(l + b) 2(l + b)
2(l + b) = 180
⇒ 2(4x + 5x) = 180
⇒ 2(9x) = 180
⇒ 18x = 180
⇒ x = 10
$\therefore$ Length = 4x cm = 4 × 10 = 40cm.
Breadth = 5x cm = 5 × 10 = 50cm.

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Question 23 Marks

The diagonals of a rhombus are 16 cm and 12 cm . Find the length of each side of the rhombus.

Answer

All the sides of a rhombus are equal in length.
The diagonals of a rhombus intersect at $90^{\circ}$.
The diagonal and the side of a rhombus form right triangles.

In $\triangle APB$ :
$AB^2=AO^2+OB^2$
$=82+62$
$=64+36$
$=100$
$AB=10 cm,$
Therefore, the length of each side of the rhombus is 10 cm .

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Question 33 Marks

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the measure of each angle.

Answer

Let the angles be (x)º, (2x)º, (3x)º and (4x)º. (x)º, (2x)º, (3x)º and (4x)º.
Sum of the angles of a quadrilateral is 360º.
x + 2x + 3x + 4x = 360
10x = 360
$\text{x}=\frac{360}{10}$
x = 36
(2x)º = (2 × 36)º = 72º
(3x)º = (3 × 36)º = 108º
(4x)º = (4 × 36)º = 144º
The angles of the quadrilateral are 36º, 72º, 108º and 144º. 36º, 72º, 108º and 144º.

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Question 43 Marks

Two adjacent angles of a parallelogram are in the ratio 2 : 3. Find the measure of each of its angles.

Answer

Let the two adjacent angles of the parallelogram be (2x)º and (3x)º.
Sum of any two adjacent angles of a parallelogram is 180º.
$\therefore$ 2x + 3x = 180
⇒ 5x = 180
⇒ x = 36
(2x)º = (2 × 36)º = 72º
(3x)º = (3 × 36)º = 108º
Measures of the angles are 72º and 108º.

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Maths 3 Mark Question

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