Question

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

Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that encloses his rectangular front yard. The length, the side along the house, is five feet less than three times the width. Find the length and width of the fencing.

Short answer

The measure of length and width of the fencing are $118,41$feet respectively.

Step-by-step solution

Step 1. Given Information 

The given data is that Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that encloses his rectangular front yard. The length, the side along the house, is five feet less than three times the width.

Step 2. Calculation 

Let L be the length and W be the width.

The length is five feet less than three times the width that is $L=3W-5--\left(1\right)$

The fencing is taken for the three sides of the yard and length of garland is 200 that is $L+2W=200--\left(2\right)$

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

localid="1656375558529" $$\begin{gathered} 3W-5+2W=200 \\ 5W=205 \\ W=\frac{205}{5} \\ W=41 \end{gathered}$$

Substitute the value of W in equation (1) to obtain the value of L.

localid="1656375594456" $$\begin{gathered} L=3\left(41\right)-5 \\ L=123-5 \\ L=118 \end{gathered}$$