Question

Geometry Express the area A of a rectangle as a function of the length x if the length of the rectangle is twice its width.

Short answer

The area of rectangle is$A\left(x\right)=2x^2$.

Step-by-step solution

Step 1. Given Information

In the given question we have to express the area A of a rectangle as a function of the length xif the length of the rectangle is twice its width.

Step 2. We know that the area of Rectangle A=l×bwhere, src="data:image/svg+xml;base64,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" role="math" localid="1646314813700" src="assets/icons/image_placeholder.svg" style="width:30%" src="assets/icons/image_placeholder.svg" style="width:30%" src="assets/icons/image_placeholder.svg" style="width:30%" l=Length, b=breadth

Let $x=$width of a rectangle.

So the length of a rectangle is

$l=2x$

Step 3. Putting the value of l and b

$$\begin{gathered} A\left(x\right)=2x\times x \\ A\left(x\right)=2x^2 \end{gathered}$$