Question

question 25 (1 point) a rectangle has length $sqrt{50}$ and width $sqrt{40}$. what is the perimeter of the rectangle? a) $10sqrt{2}+4sqrt{10}$ b) $5sqrt{2}+2sqrt{10}$ c) $6sqrt{5}$ d) $20sqrt{5}$

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is length and $w$ is width. Here, $l=\sqrt{50}$ and $w = \sqrt{40}$. So $P=2(\sqrt{50}+\sqrt{40})$.

Step2: Simplify square - roots

Simplify $\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$ and $\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}$.

Step3: Substitute simplified values

Substitute into the perimeter formula: $P = 2(5\sqrt{2}+2\sqrt{10})$.

Step4: Distribute the 2

$P=2\times5\sqrt{2}+2\times2\sqrt{10}=10\sqrt{2}+4\sqrt{10}$.

Answer:

A. $10\sqrt{2}+4\sqrt{10}$