Question

Draw five triangles and measure their sides. Check-in each case, if the sum of the lengths of any two sides is always less than the third side.

Answer 1

Case 1. Let us draw a triangle ABC

AB = 2.5 cm

BC = 4.8 cm and

AC = 5.2 cm

AB + BC = 2.5 cm + 4.8 cm

= 7.3 cm

As 7.3 > 5.2

∴ AB + BC > AC

Thus, we observe that the sum of any two sides of a triangle is greater than the third side.

Case 2. Let us draw a triangle PQR

PQ = 2 cm

QR = 2.5 cm

PR = 3.5 cm

PQ + QR = 2 cm + 2.5 cm

= 4.5 cm

As 4.5 > 3.5

∴ PQ + QR > PR

Thus, we observe that the sum of any two sides of a triangle is greater than the third side.

Case 3. Let us draw triangle XYZ

XY = 5 cm

YZ = 3 cm

ZX = 6.8 cm

XY + YZ = 5 cm + 3 cm

= 8 cm

As 8 > 6.8

∴ XY + YZ > ZX

Thus, we observe that the sum of any two sides of a triangle is greater than the third side.

Case 4. Let us draw a triangle MNS

MN = 2.7 cm

NS = 4 cm

MS = 4.7 cm

MN + NS = 2.7 cm + 4 cm

6.7 cm

As 6.7 > 4.7

∴ MN + NS > MS

Thus, we observe that the sum of any two sides of a triangle is greater than the third side.

Case 5. Let us draw a triangle KLM

KL = 3.5 cm

LM = 3.5 cm

KM = 3.5 cm

KL + LM = 3.5 cm + 3.5 cm

= 7 cm

As 7 cm > 3.5 cm

∴ KL + LM > KM

Thus, we observe that the sum of any two sides of a triangle is greater than the third side.

Therefore we conclude that the sum of any two sides of a triangle is always greater than the third side.