Question

find the area of the following rectangle. give your answer in simplest form.
show your work here.
hint: to add the square root symbol (√), type
oot\

Explanation:

Step1: Recall area formula for rectangle

The area formula of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l = 4\sqrt{30}$ and $w=2\sqrt{60}$.

Step2: Multiply the length and width

$A=(4\sqrt{30})\times(2\sqrt{60})$. Using the property $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$ and $a\sqrt{c}\times b\sqrt{d}=ab\sqrt{cd}$, we have $A = 4\times2\times\sqrt{30\times60}$.

Step3: Simplify the product inside the square - root

First, calculate $30\times60 = 1800$. So $A = 8\sqrt{1800}$.

Step4: Simplify the square - root

We can rewrite $1800$ as $36\times50$. Then $\sqrt{1800}=\sqrt{36\times50}=\sqrt{36}\times\sqrt{50}=6\sqrt{50}$. And $\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$. So $\sqrt{1800}=6\times5\sqrt{2}=30\sqrt{2}$.

Step5: Calculate the final area

Substitute $\sqrt{1800}=30\sqrt{2}$ into $A = 8\sqrt{1800}$, we get $A=8\times30\sqrt{2}=240\sqrt{2}$.

Answer:

$240\sqrt{2}$