Question

In the following exercises, translate to a system of equations and solve.

The perimeter of a rectangular toddler play area is 100 feet. The length is ten more than three times the width. Find the length and width of the play area.

Short answer

The measure of length and width of the rectangle are 40, 10 feet respectively.

Step-by-step solution

Step 1. Given Information  

The given data is that the perimeter of a rectangular toddler play area is 100 feet. The length is ten more than three times the width.

Step 2. Calculation   

Let x be the length and y be the width.

The length is ten more than three times the width that is $x=3y+10--\left(1\right)$

The perimeter of rectangle is 100 feet that is$2x+2y=100--\left(2\right)$

Solve the equations by substituting equation (1) in equation (2) to find the value of y.

$$\begin{gathered} 2(3y+10)+2y=100 \\ 6y+20+2y=100 \\ 8y=80 \\ y=10 \end{gathered}$$

Substitute the value of y in equation (1) to obtain the value of x.

$$\begin{gathered} x=3\left(10\right)+10 \\ x=30+10 \\ x=40 \end{gathered}$$