Question

question 21 (1 point) find a simplified expression for the perimeter of this shape. not to scale. 4\sqrt{2}+1 \sqrt{3}-\sqrt{2} a) 4\sqrt{6}+\sqrt{3}-8 - \sqrt{2} b) 3\sqrt{2}+\sqrt{3}+1 c) 6\sqrt{2}+2\sqrt{3}+2 d) 12\sqrt{2}+4\sqrt{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 $w = \sqrt{3}-\sqrt{2}$.

Step2: Substitute values into formula

$P=2((4\sqrt{2}+1)+(\sqrt{3}-\sqrt{2}))$.

Step3: Simplify the expression inside the parentheses

$(4\sqrt{2}+1)+(\sqrt{3}-\sqrt{2})=(4\sqrt{2}-\sqrt{2})+\sqrt{3}+1 = 3\sqrt{2}+\sqrt{3}+1$.

Step4: Multiply by 2

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

Answer:

c) $6\sqrt{2}+2\sqrt{3}+2$