Question

The perimeter of the rectangle shown is 28 units. The length is 10 units. What is the width of the rectangle?

1. Write an equation for the perimeter of the rectangle in terms of x.
2. Solve the equation to find the value of x.
3. Find the width of the rectangle using the value of x.

Check your answer.

Short answer

1. The equation is$28=2\left(10+x+2\right)$ .
2. The solution is$x=2$ .

The width of the rectangle is$4$ units.

Step-by-step solution

Part a. Step 1 – Given information.

A rectangle of perimeter 28 units with length 10 units and width (x + 2).

– Write the formula.

The perimeter of the rectangle is given by,

$P=2\left(l+w\right)$

Here l is the length and w is the width of the rectangle.

– Write the equation.

Perimeter = 28 units

Length = 10 units

Width = (x + 2)

Substitute the values in the formula,

$\begin{array}{l}28=2\left(10+\left(x+2\right)\right)\\ 28=2\left(10+x+2\right)\end{array}$

This is the required equation.

Part b. Step 1 – Given information.

A rectangle of perimeter 28 units with length 10 units and width (x + 2).

– Solve the equation.

The equation$28=2\left(10+x+2\right)$ can be solved in below.

$\begin{array}{l}28=2\left(10+x+2\right)\\ 28=20+2x+4\end{array}$

Combine the constant terms,

$\begin{array}{c}28=24+2x\\ 24+2x=28\end{array}$

Subtract 24 from both sides,

$\begin{array}{c}24+2x-24=28-24\\ 2x=4\end{array}$

Divide by 2 on both sides,

$\begin{array}{c}\frac{2x}{2}=\frac{4}{2}\\ x=2\end{array}$

Part c. Step 1 – Given information.

A rectangle of perimeter 28 units with length 10 units and width (x + 2).

– Determine the width.

Substitute the value of x in the expression of width to find its value,

$\begin{array}{c}x+2=2+2\\ =4\end{array}$

Hence, the width of the rectangle is 4 units.

Part d. Step 1 – Given information.

A rectangle of perimeter 28 units with length 10 units and width (x + 2).

The solution of the equation$28=2\left(10+\left(x+2\right)\right)$is$x=2$ .

– Check the solution.

Substitute all the values in the formula,

$\begin{array}{c}P=2\left(l+w\right)\\ 28=2\left(10+4\right)\\ 28=2\left(14\right)\\ 28=28\end{array}$