The three side lengths of four triangles are given. Which triangle is a right triangle?

To determine which triangle is a right triangle, we can use the Pythagorean theorem. A triangle is a right triangle if the square of the longest side is equal to the sum of the squares of the other two sides.

Let’s check each triangle:

1. Triangle 1: √13, 6, 7

Longest side = 7

( 7^2 = 49 )

( (√13)^2 + 6^2 = 13 + 36 = 49 )

Yes, this is a right triangle.

2. Triangle 2: 7, 8, 13

Longest side = 13

( 13^2 = 169 )

( 7^2 + 8^2 = 49 + 64 = 113 )

Not a right triangle.

3. Triangle 3: 10, 11, 12

Longest side = 12

( 12^2 = 144 )

( 10^2 + 11^2 = 100 + 121 = 221 )

Not a right triangle.

4. Triangle 4: √10, 9, 8

Longest side = 9

( 9^2 = 81 )

( (√10)^2 + 8