# A triangle has sides with lengths of 12 meters, 35 meters, and 37 meters. Is it a right triangle?

Nov 28, 2016

Because $1369 = 1369$ is equal this is a right triangle.

#### Explanation:

If this is a right triangle we can then substitute the sides of the triangle (12 and 35) and the hypotenuse (37) into the Pythagoras Theorem and the two sides of the equation will be equal. If this is not a right triangle the two sides of the equation will not be equal.

The Pythagoras Theorem is ${a}^{2} + {b}^{2} = {c}^{2}$

Substituting we get:

${12}^{2} + {35}^{2} = {37}^{2}$

$12 \cdot 12 + 35 \cdot 35 = 37 \cdot 37$

$144 + 1225 = 1369$

$1369 = 1369$

Because these are equal this is a right triangle.