# Do the following sets of sides of a triangle satisfy the Pythagorean Theorem: 8,24,25?

May 16, 2016

No. The square of the hypotenuse is not equal to the sum of the squares of the other two sides. Therefore, the sides 8, 24, and 25 do not satisfy the Pythagorean theorem.

#### Explanation:

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The hypotenuse is always the longest side of a right triangle. The equation for the Pythagorean theorem is ${a}^{2} + {b}^{2} = {c}^{2}$.

Substituting 8, 24, 25 for a, b, and c, we get:

${8}^{2} + {24}^{2} = {25}^{2}$

Simplify.

$64 + 576 = 625$

Simplify.

$640 \ne 625$

The square of the hypotenuse is not equal to the sum of the squares of the other two sides. Therefore the sides 8, 24, and 25 do not satisfy the Pythagorean theorem.