Question

The width of a rectangular garden is 9 feet longer than 4 times its length. If the garden's perimeter is178 feet, what are the dimensions of the garden?Length =feetWidth =feet

Answer 1

Let x be the length and y be the width of the rectangle.

It is given that width of a rectangular garden is 9 feet longer than 4 times its length so it follows:

$\begin{gathered} y=9+4x \\ 4x-y=-9\ldots(i) \end{gathered}$

It is also given that the garden's perimeter is 178 feet so it follows:

$\begin{gathered} 2(x+y)=178 \\ x+y=89\ldots(ii) \end{gathered}$

Add (i) and (ii) to get:

$\begin{gathered} 4x-y=-9 \\ + \\ x+y=89 \\ 5x=80 \\ x=16 \end{gathered}$

Substitute x=16 in (ii) to get:

$\begin{gathered} 16+y=89 \\ y=73 \end{gathered}$

Hence it follows that:

Length = 16 feet

Width =73 feet.