Which set of numbers could represent the lengths of the sides of a right triangle?
12, 18, 22
8, 15, 17
7, 9, 11
10, 15, 20
You need a^2 + b^2 = c^2
so test the choices.
To determine if a set of numbers could represent the lengths of the sides of a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side.
Let's apply the theorem to each set of numbers:
1. Set: 12, 18, 22
Using the theorem:
12^2 + 18^2 = 144 + 324 = 468
22^2 = 484
Since 468 is not equal to 484, this set of numbers does not represent the lengths of the sides of a right triangle.
2. Set: 8, 15, 17
Using the theorem:
8^2 + 15^2 = 64 + 225 = 289
17^2 = 289
The sum of the squares of the two shorter sides is equal to the square of the longest side. So, this set of numbers represents the lengths of the sides of a right triangle.
3. Set: 7, 9, 11
Using the theorem:
7^2 + 9^2 = 49 + 81 = 130
11^2 = 121
Since 130 is not equal to 121, this set of numbers does not represent the lengths of the sides of a right triangle.
4. Set: 10, 15, 20
Using the theorem:
10^2 + 15^2 = 100 + 225 = 325
20^2 = 400
Since 325 is not equal to 400, this set of numbers does not represent the lengths of the sides of a right triangle.
So, the only set of numbers that represents the lengths of the sides of a right triangle is 8, 15, 17.