Question

question 4 (1 point) find a simplified expression for the perimeter of this shape. not to scale. 4√2 + 1 √6 - √2 a) 4√6+√3 - 8 - √2 b) 6√2+2√3 + 2 c) 3√2+√3 + 1 d) 12√2+4√3 + 4

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=4\sqrt{2}+1$ and $w = \sqrt{6}-\sqrt{2}$.

Step2: Substitute values into formula

$P=2((4\sqrt{2}+1)+(\sqrt{6}-\sqrt{2}))$.

Step3: Simplify inside the parentheses

First, combine like - terms inside the parentheses: $(4\sqrt{2}+1)+(\sqrt{6}-\sqrt{2})=(4\sqrt{2}-\sqrt{2})+\sqrt{6}+1 = 3\sqrt{2}+\sqrt{6}+1$.

Step4: Multiply by 2

$P = 2(3\sqrt{2}+\sqrt{6}+1)=6\sqrt{2}+2\sqrt{6}+2$.

Answer:

B. $6\sqrt{2}+2\sqrt{6}+2$