Question

area the length of a rectangle measures 8\sqrt{12} centimeters and the width measures 4\sqrt{8} centimeters. what is the area of the rectangle? o a) 18\sqrt{12} cm² o b) 128\sqrt{6} cm² o c) 128\sqrt{6} m² o d) 24\sqrt{6} cm²

Explanation:

Step1: Recall area formula

The area formula of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l = 8\sqrt{12}$ and $w = 4\sqrt{8}$. So $A=8\sqrt{12}\times4\sqrt{8}$.

Step2: Multiply coefficients and radicals separately

Multiply the coefficients $8\times4 = 32$, and multiply the radicals $\sqrt{12}\times\sqrt{8}=\sqrt{12\times8}=\sqrt{96}$. So $A = 32\sqrt{96}$.

Step3: Simplify the radical

Simplify $\sqrt{96}=\sqrt{16\times6}=4\sqrt{6}$. Then $A=32\times4\sqrt{6}$.

Step4: Calculate the final result

$32\times4\sqrt{6}=128\sqrt{6}$, and the unit is $\text{cm}^2$ (since the lengths are in cm).

Answer:

B. $128\sqrt{6}\text{ cm}^2$