Which set of numbers could represent the lengths of the sides of a right triangle?

a.) 8, sqrt57, 11

b.) 6, sqrt7, 13

c.) 4, sqrt31, 9

d.) 11, sqrt42, 13

In order to solve this, first we need to square all of these options, and then see whether the largest number is the sum of the two smaller ones. Here's how to do it:

A. 8, √57, 11; when you square all of them, you get: 64, 57, 121

64 + 57 = 121, which means A is the correct answer. But let's take a look at the other options too.

B: 6, √7, 13; 36, 7, 169

36 + 7 = 43, and not 169, which means B is incorrect

C: 4, √31, 9 = 16, 31, 81

16 + 31 = 47, and not 81, which means C is incorrect

D: 11, √42, 13 = 121, 42, 169

121 + 42 = 163, and not 169, which means D is incorrect.

The correct answer is A. 8, sqrt57, 11