# How do you use the Pythagorean Theorem to determine if the three sides are a right triangle: 15 m, 12 m, 9m?

${9}^{2} + {12}^{2} = 81 + 144 = 225 = {15}^{2}$
Actually, we could have noticed that all the sides are a multiple of 3m, namely $5 \times 3$m, $4 \times 3$m and $3 \times 3$m, so we have a 3,4,5 triangle - just 3 times larger.
${3}^{2} + {4}^{2} = 9 + 16 = 25 = {5}^{2}$