Question

Express the given quantity in terms of the indicated variable.

The area (in${\text{ft}}^{\text{2}}$) of a rectangle that is four times as long as it is wide; w = width of the rectangle (in ft)

Short answer

The area of the rectangle is$4w^2$ square feet.

Step-by-step solution

Step 1. Concept used.

The area of the rectangle can be computed by multiplying the length and width.

Step 2. Plug the values in the formula.

Here, length$=4w$

The area of the rectangle is

$A=lw$

Plug the values:

$A=w\left(4w\right)$

Step 3. Calculate the area.

Multiply

$A=4w\cdot w$

Apply power rule: $a^m\times a^n=a^{m+n}$

$\begin{array}{l}A=4w^{1+1}\\ A=4w^2\end{array}$