Question

in a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. if a = 36 kilometers and b = 48 kilometers, what is the perimeter? if necessary, round to the nearest tenth.

Explanation:

Step1: Find the hypotenuse length

Use the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 36$ and $b = 48$:
$c=\sqrt{36^{2}+48^{2}}=\sqrt{1296 + 2304}=\sqrt{3600}=60$

Step2: Calculate the perimeter

The perimeter $P=a + b + c$. Substitute $a = 36$, $b = 48$ and $c = 60$:
$P=36+48 + 60=144$

Answer:

$144.0$