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

**Solution:**

We will be using the concept of triangles to solve this.

Case I. In ∆ABC

Consider AB = 2.5 cm, BC = 4.8 cm and AC = 5.2 cm

AB + BC = 2.5 cm + 4.8 cm = 7.3 cm

Since, 7.3 > 5.2 , AB + BC > AC

Therefore, the sum of any two sides of a triangle is greater than the third side.

Case II. In ∆PQR,

Consider PQ = 2 cm, QR = 2.5 cm and PR = 3.5 cm

PQ + QR = 2 cm + 2.5 cm = 4.5 cm

Since, 4.5 > 3.5, PQ + QR > PR

Therefore, the sum of any two sides of a triangle is greater than the third side.

Case III. In ∆XYZ,

Consider XY = 5 cm, YZ = 3 cm and ZX = 6.8 cm

XY + YZ = 5 cm + 3 cm = 8 cm

Since, 8 > 6.8, XY + YZ > ZX

Therefore, the sum of any two sides of a triangle is greater than the third side.

Case IV. In ∆MNS,

Consider MN = 2.7 cm, NS = 4 cm and MS = 4.7 cm

MN + NS = 2.7 cm + 4 cm = 6.7 cm

Since, 6.7 >4.7, MN + NS > MS

Hence, the sum of any two sides of a triangle is greater than the third side.

Case V. In ∆KLM,

Consider KL = 3.5 cm, LM = 3.5 cm and KM = 3.5 cm

KL + LM = 3.5 cm + 3.5 cm = 7 cm

7 cm > 3.5 cm, KL + LM > KM

Therefore, the sum of any two sides of a triangle is greater than the third side. Hence, we conclude that the sum of any two sides of a triangle is never less than the third side.

NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.1 Question 7

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

**Summary:**

Five triangles are drawn and their sides are measured and in each case, we see that the sum of any two sides of a triangle is greater than the third side.

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