# A triangle has sides with lengths of 36 yards, 47 yards, and 30 yards. Is it a right triangle?

Nov 29, 2016

$2196 \ne 2209$ so this is not a right triangle.

#### Explanation:

If this is a right triangle then substituting the sides of the triangle (30 and 36) and the hypotenuse (47) into the Pythagorean Theorem will calculate to both sides of the equation being equal. If they are not equal then this is not a right triangle.

The Pythagorean Theorem is:

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

Substituting and calculating gives:

${30}^{2} + {36}^{2} = {47}^{2}$

$900 + 1296 = 2209$

$2196 \ne 2209$ so this is not a right triangle.