Question

Construct a triangle with length of 3 sides
as follows:
A. 5 cm, 4.5 cm, 3.5 cm
B. 5.5 cm, 5 cm, 4 cm
C. 3.5 cm, 5 cm, 6 cm
D. 7 cm, 6 cm, 5 cm​

Answer 1

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Construct a triangle with length of 3 sides as follows:

A. 5 cm, 4.5 cm, 3.5 cm

B. 5.5 cm, 5 cm, 4 cm

C. 3.5 cm, 5 cm, 6 cm

D. 7 cm, 6 cm, 5 cm

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Attached

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What do you mean by a triangle?

Ans ☞ A triangle is a polygon made up of the least number of sides ( 3 line segments )

How do you construct a triangle with three given sides?

Ans ☞ To construct a triangle when the lengths of all the three sides are given, we must need the following mathematical instruments :

1. Ruler

2. Compass

For example :

Construct a triangle ABC given that AB = 4cm, BC = 6 cm and AC = 5 cm.

Given measurements :

AB = 4 cm

BC = 6 cm

AC = 5 cm

Step 1 : Draw a line segment BC = 6cm

( Here we take the longest side )

Step 2 : With ‘B’ as centre, draw an arc of radius 4 cm above the line BC.

Step 3 : With ‘C’ as center, draw an arc of 5 cm to intersect the previous arc at ‘A’

Step 4 : Join AB and AC.

Now ABC is the required triangle.

This construction clearly shows how to construct a triangle when the lengths of all the three sides are given with compass and straightedge or ruler. ( Refer the attachment )

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Important Property of Triangle -

"The sum of any two sides of a triangle is always greater than the third side"

If the above mentioned property of triangle is not met by the given three sides, we will not be able to construct a triangle with those three sides.