Question

what is the perimeter? if necessary, round to the nearest tenth. feet

Explanation:

Step1: Find the base using Pythagorean theorem

Let the hypotenuse be $c = 20$ ft and one - leg be $a = 16$ ft. According to the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, so $b=\sqrt{c^{2}-a^{2}}$. Substitute $c = 20$ and $a = 16$ into the formula: $b=\sqrt{20^{2}-16^{2}}=\sqrt{(20 + 16)(20 - 16)}=\sqrt{36\times4}=\sqrt{144}=12$ ft.

Step2: Calculate the perimeter

The perimeter $P$ of a triangle is the sum of the lengths of its sides. So $P=12 + 16+20$.
$P = 48$ ft.

Answer:

48