Question

9) John is hanging 146 feet of Halloween lights on the sides of his rectangular fence that

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.