Question

What set of three numbers could represent the lengths of the side of a right triangle?

A.) 8, 12, 16
B.) 6, 7, 8
C.) 5, 12, 13
D.) 16, 32, 36

Answer 1

C.) 5, 12, 13

Explanation:

In a right triangle, the sum of the squares of the two shorter sides must equal the square of the longest side (Pythagoras).

a² + b² = c²

We can test each set of numbers to see which one fits.

A.) 8² + 12² = 16²

64 + 144 = 256

208 ≠ 256

B.) 6² + 7² = 8²

36 + 49 = 64

85 ≠ 64

C.) 5² + 12² = 13²

25 + 144 = 169

169 = 169

The numbers 5, 12, and 13 could represent the lengths of the sides of a right triangle.

D.) 16² + 32² = 36²

256 + 1024 = 1296

1280 ≠ 1296