Question

9) John is hanging 146 feet of Halloween lights on the sides of his rectangular fence that
encloses his property. The length is five feet less than five times the width. Find the length
of the fencing.

Answer 1

Answer:

The length of the fencing is 60 feet.

Explanation:

At first we remember that the perimeter formula of the rectangular fence is represented by:

$p = 2\cdot (w+l)$ (1)

Where:

$w$ - Width, measured in feet.

$l$ - Length, measured in feet.

$p$ - Perimeter, measured in feet.

From statement, we know the following relation:

$l = 5\cdot w -5$ (2)

By applying (2) in (1) we expand the equation above:

$p = 2\cdot (w+5\cdot w -5)$

$p = 2\cdot (6\cdot w -5)$

$p = 12\cdot w - 10$

If we know that $p = 146$, the width of the fencing is:

$12\cdot w = p+10$

$w = \frac{p+10}{12}$

$w = \frac{156}{12}$

$w = 13\,ft$

And the length of the fencing is:

$l = 5\cdot (13) -5$

$l = 60\,ft$

The length of the fencing is 60 feet.