Download App

Maths 3 Mark Question

Triangles and their Properties · Maharashtra Board STD 6 (MSBSHSE - Semi English Medium). 6 questions.

Questions

3 Mark Question

Take a timed test

6 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
The lengths of the three segments are given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.
i. 17 cm, 7 cm, 8 cm
ii. 7 cm, 24 cm, 25 cm
iii. 9 cm, 6 cm, 16 cm
iv. 8.4 cm, 16.4 cm, 4.9 cm
v. 15 cm, 20 cm, 25 cm
vi. 12 cm, 12 cm, 16 cm
Answer
i. The lengths of the three sides are 17 cm, 7 cm, 8 cm.
a. 7 cm + 17 cm = 24 cm, greater than 8 cm
b. 8 cm +17 cm = 25 cm, greater than 7 cm
c. 7 cm + 8 cm =15 cm, not greater than 17 cm
The sum of lengths of two sides in (c) is not greater than the length of the third side.
∴ Triangle cannot be drawn with sides 17 cm, 7 cm, 8 cm.

ii. The lengths of the three sides are 7 cm, 24 cm, 25 cm.
a. 7 cm + 24 cm = 31 cm, greater than 25 cm
b. 25 cm + 7 cm = 32 cm, greater than 24 cm
c. 24 cm + 25 cm = 49 cm, greater than 7 cm
The sum of lengths of two sides is greater than the length of the third side.
∴ Triangle can be drawn with sides 7 cm, 24 cm, 25 cm.

iii. The lengths of the three sides are 9 cm, 6 cm, 16 cm.
a. 9 cm + 16 cm = 25 cm, greater than 6 cm
b. 6 cm + 16 cm = 22 cm, greater than 9 cm
c. 9 cm+ 6 cm =15 cm, not greater than 16 cm
The sum of lengths of two sides in (c) is not greater than the length of the third side.
∴ Triangle cannot be drawn with sides 9 cm, 6 cm, 16 cm.

iv. The lengths of the three sides are 8.4 cm, 16.4 cm, 4.9 cm.
a. 8.4 cm + 16.4 cm = 24.8 cm, greater than 4.9 cm
b. 4.9 cm + 16.4 cm = 21.3 cm, greater than 8.4 cm
c. 8.4 cm + 4.9 cm = 13.3 cm, not greater than 16.4 cm
The sum of lengths of two sides in (c) is not greater than the length of the third side.
∴ Triangle cannot be drawn with sides 8.4 cm, 16.4 cm, 4.9 cm.

v. The lengths of the three sides are 15 cm, 20 cm, 25 cm.
a. 15 cm + 20 cm = 35 cm, greater than 25 cm
b. 25 cm + 20 cm = 45 cm, greater than 15 cm
c. 15 cm + 25 cm = 40 cm, greater than 20 cm
The sum of lengths of two sides is greater than the length of the third side.
∴ Triangle can be drawn with sides 15 cm, 20 cm, 25 cm.

vi. The lengths of the three sides are 12 cm, 12 cm, 16 cm.
a. 12 cm + 12 cm = 24 cm, greater than 16 cm
b. 12 cm + 16 cm = 28 cm, greater than 12 cm
c. 12 cm + 16 cm = 28 cm, greater than 12 cm
The sum of lengths of two sides is greater than the length of the third side.
∴ Triangle can be drawn with sides 12 cm, 12 cm, 16 cm.

View full question & answer→
Question 23 Marks
The lengths of the sides of some triangles are given. Say what types of triangles they are.
  1. 3 cm, 4 cm, 5 cm
  2. 3.4 cm, 3.4 cm, 5 cm
  3. 4.3 cm, 4.3 cm, 4.3 cm
  4. 3.7 cm, 3.4 cm, 4 cm
Answer
  1. Since, no two sides have equal lengths, the given triangle is a scalene triangle.
  2. Since, two sides have equal length, the given triangle is an isosceles triangle.
  3. Since, all the three sides have equal lengths, the given triangle is an equilateral triangle.
  4. Since, no two sides have equal lengths, the given triangle is a scalene triangle.
View full question & answer→
Question 33 Marks
As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way is shorter? Explain why.

Image

Answer
The two roads which Avinash can choose to go to school are

  1. Road AB + Road BC
  2. Road AC

The three roads together form ∆ABC.
Road AC is shorter because the sum of the lengths of any two sides (side AB + side BC) of a triangle is always greater than the third side (side AC).

View full question & answer→
Question 43 Marks
Observe the figures below and write the type of the triangle based on its sides:

Image

Answer
i. equilateral
ii. scalene
iii. isosceles
View full question & answer→
Question 53 Marks
Observe the figures below and write the type of the triangle based on its angles:

Image

Answer
i. right angled
ii. Obtuse angled
iii. acute angled
View full question & answer→
Question 63 Marks
Measure the sides of the following triangles in centimeters, using a divider and ruler. Enter the lengths in the table below. What do you observe?
Image
In ∆ABCIn ∆PQRIn ∆XYZ
l (AB) = cml (QR) = cml (XY) = cm
l (BC) = cml (PQ) = cml (YZ) = cm
l (AC) = cml (PR) = cml (XZ) = cm
Answer
In ∆ABCIn ∆PQRIn ∆XYZ
l (AB) = 2.6 cml (QR) = 2.8 cml (XY) = 2.8 cm
l (BC) = 2.6 cml (PQ) = 3.8 cml (YZ) = 2.6 cm
l (AC) = 2.6 cml (PR) = 3.8 cml (XZ) = 4.3 cm

We observe that,

  1. ∆ABC is an equilateral triangle,
  2. ∆PQR is an isosceles triangle, and
  3. ∆XYZ is a scalene triangle.
View full question & answer→
Generate Paper FreeAll Triangles and their Properties topics