Question

Write an algebraic expression to represent the perimeter of the rectangle and then evaluate it to find the perimeter when $w=8\text{\hspace{0.17em}\hspace{0.17em}cm}$.

Short answer

The perimeter of the rectangle is $74\text{\hspace{0.17em}\hspace{0.17em}cm}$.

Step-by-step solution

Step 1. Given information.

The length of the rectangle is $4w-3$.

And the width of the rectangle is w.

Step 2. Write the Formula.

The perimeter of a rectangle is given by:

$P=2\left(\text{Length}+\text{Width}\right)$

Step 3. Write the expression for perimeter.

The expression is:

$\begin{array}{c}P=2\left(\text{Length}+\text{Width}\right)\\ =2\left[\left(4w-3\right)+w\right]\end{array}$

Step 4. Simplify the expression.

The expression for the perimeter is:

$P=2\left[\left(4w-3\right)+w\right]$

Substitute $w=8\text{\hspace{0.17em}\hspace{0.17em}cm}$in the above expression.

$\begin{array}{c}P=2\left[\left(4\times 8-3\right)+8\right]\\ =2\left[\left(32-3\right)+8\right]\\ =2\left[29+8\right]\\ =2\left[37\right]\\ =74\text{\hspace{0.17em}\hspace{0.17em}cm}\end{array}$