Which three lengths could be the lengths of the sides of a triangle? Question 23 options: 21 cm, 7 cm, 6 cm 12 cm, 5 cm, 17 cm 9 cm, 22 cm, 11 cm 10 cm, 15 cm, 24 cm

Answer: option d is the correct answer

Step-by-step explanation:

Looking at the different lengths given,

It is only the the last set containing

10 cm, 15 cm, 24 cm that can be the sides of a triangle.

This can be proven by finding the area of the triangle with the sides given. Considering

10 cm, 15 cm, 24 cm

Perimeter = 10+15+24 = 49

Semi perimeter, s = 49/2 = 24.5

Area = √s (s-a) (s-b) (s-c) = √24.5 (24.5-10) (24.5-15) (24.5-24) = √24.5 * 14.5 * 9.5 * 0.5 = √1687.4375 = 41.07843108007

If we try finding the area for the other given lengths,

Considering

1) 21 cm, 7 cm, 6 cm

s = 17

Looking for the area like we just did will lead to square root of a negative number (17-24 = - 7) and the area cannot be determined.

2) 12 cm, 5 cm, 17 cm

s = 17

Looking for the area like we did previously, the area will be zero (17-17 = 0) and this is impossible.

3) 9 cm, 22 cm, 11 cm

s = 21

Looking for the area like we did previously will lead to square root of a negative number (21-22 = - 1) and the area cannot be determined.

In conclusion, the three lengths that could be the lengths of the sides of a triangle are 10 cm, 15 cm, 24 cm