# A triangle has sides with lengths of 25 miles, 45 miles, and 52 miles. Is it a right triangle?

Dec 3, 2016

$2650 \ne 2704$ therefore this is not a right triangle.

#### Explanation:

To do determine if this is a right triangle you need to substitute the sides of the triangle (25 and 45) and the hypotenuse (52) into the Pythagorean Theorem and determine if each side of the equation are equal. If they are equal it is a right triangle. If they are not equal it is not a right triangle.

The Pythagorean Theorem is:

${a}^{2} + {b}^{2} = {c}^{2}$

Substituting and calculating gives:

${25}^{2} + {45}^{2} = {52}^{2}$

$625 + 2025 = 2704$

$2650 \ne 2704$