Question

A rectangle has a length that is 15 more than 3 times its width. The total area of the rectangle is 72 square feet.If the width is represented by w, write an equation that could be used to solve for the width.

Answer 1

Let's begin by listing out the given information:

This is a rectangle. It has a length & width

The total area of the rectangle is 72 square feet

Its length is 15 more than 3 times its width

Mathematically,

`\begin{gathered} Length=15+3\cdot w \\ Length=15+3w \end{gathered}`

Now, the area of a rectangle is given by the product of the length & width

`\begin{gathered} Area=length* width \\ Area=72 \\ length=15+3w \\ width=w \\ \Rightarrow72=(15+3w)* w \\ 72=15w+3w^2 \\ \text{Rearranging the equation, we have:} \\ 3w^2+15w-72=0 \end{gathered}`