Question

The width of a rectangle is three more than twice the length. The perimeter is $96$inches. Find the length and the width.

Short answer

The length and width of the given rectangle is $15inches$and $33inches$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

Perimeter of the given rectangle is $96inches$.

Step 2. Find the length and the width.

Assume l and w to be the length and width of the rectangle. Then,

$w=3+2l$

We know the formula of the perimeter of the rectangle is given below,

$$\begin{gathered} P=2\left(l+w\right)......\left(i\right) \\ 96=2\left\{l+\left(3+2l\right)\right\} \\ 48=3l+3 \\ l=15inches \end{gathered}$$

Then,

$$\begin{gathered} w=3+2\left(15\right) \\ w=3+30 \\ w=33inches \end{gathered}$$

Step 3. Check the answer.

Substitute the values in equation (i),

$$\begin{gathered} P=2\left(15+33\right) \\ P=2\left(48\right) \\ P=96inches \end{gathered}$$

Hence, the values of the length and width obtained is correct.