Answer: option d is the correct answer
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