Question

write expressions for the perimeter and area for the figure. then simplify these expressions. assume that all measures are given in inches.
the perimeter is (square) inches.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Simplify $\sqrt{125}$

$$\sqrt{125}=\sqrt{25\times5}=5\sqrt{5}$$

Step2: Find the perimeter formula for a rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l=\sqrt{125}+4$ and $w=\sqrt{125}-4$.
Substitute $l$ and $w$ into the formula:
$$P=2((\sqrt{125}+4)+(\sqrt{125}-4))$$

Step3: Simplify the perimeter expression

First, simplify the expression inside the parentheses:
$$(\sqrt{125}+4)+(\sqrt{125}-4)=2\sqrt{125}$$
Then, substitute back into the perimeter formula:
$$P = 2\times2\sqrt{125}=4\sqrt{125}$$
Since $\sqrt{125}=5\sqrt{5}$, then $P = 4\times5\sqrt{5}=20\sqrt{5}$

Answer:

$20\sqrt{5}$