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
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Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l = 5\sqrt{10}$ and $w=4\sqrt{10}$.

Step2: Multiply length and width

$A=(5\sqrt{10})\times(4\sqrt{10})$. Using the property of multiplication of square - roots $\sqrt{a}\times\sqrt{a}=a$ and the commutative and associative properties of multiplication, we have $A=(5\times4)\times(\sqrt{10}\times\sqrt{10})$.

Step3: Simplify the expression

$5\times4 = 20$ and $\sqrt{10}\times\sqrt{10}=10$. So $A = 20\times10=200$.

Answer:

200