Question

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

The perimeter of a rectangle is 84. The length is 10 more than three times the width. Find the length and width.

Short answer

The length and width of the rectangle are 34 and 8.

Step-by-step solution

Step 1. Given Information  

The given data is that the perimeter of a rectangle is 84. The length is 10 more than three times the width.

Step 2. Calculation 

Let us assume that x be the length and y be the width

The perimeter of rectangle is 84 implies that $2x+2y=84--\left(1\right)$

The length is 10 more than three times the width implies that$x=3y+10--\left(2\right)$

Substitute the value of variable x from equation (2) in equation (1).

$$\begin{gathered} 2x+2y=84 \\ 2(3y+10)+2y=84 \\ 8y+20=84 \\ 8y=84-20 \\ 8y=64 \\ y=8 \end{gathered}$$

Find the value of variable x by using the obtained value of y.

$$\begin{gathered} x=3y+10 \\ x=3\left(8\right)+10 \\ x=24+10 \\ x=34 \end{gathered}$$

Thus, the required ordered pair is$(34,8)$