Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if b = 57 meters and c = 95 meters, what is the perimeter? if necessary, round to the nearest tenth.

Explanation:

Step1: Use Pythagorean theorem

By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, so $a=\sqrt{c^{2}-b^{2}}$. Substitute $b = 57$ and $c = 95$ into the formula: $a=\sqrt{95^{2}-57^{2}}=\sqrt{(95 + 57)(95 - 57)}=\sqrt{152\times38}=\sqrt{5776}=76$.

Step2: Calculate the perimeter

The perimeter $P=a + b + c$. Substitute $a = 76$, $b = 57$, and $c = 95$ into the formula: $P=76+57 + 95=228$.

Answer:

228.0 meters