Question

Which of the triangles whose three sides are given below can be constructed?

(a) 9 m, 5 m, 3 m

(b) 10 cm, 10 cm, 4 cm [4 MARKS]

Answer 1

Each part: 2 Marks

(a) Adding up the sides, taking two at a time, we get

9 m + 5 m = 14 m > 3 m

9 m + 3 m = 12 m > 5 m

but, 5 m + 3 m = 8 m < 9 m

So we see that the sum of one pair of sides when added is not greater than the third side.

Therefore, we cannot draw a triangle with these measurements.


(b) Adding up the sides, taking two at a time, we get

10 cm + 10 cm = 20 cm > 4 cm

10 cm + 4 cm = 14 cm > 10 cm

4 cm + 10 cm = 14 cm > 10 cm

So in each case, the sum of two sides is greater than the third side.

Hence, this triangle can be constructed.