Question

All $50$ states have legislation regarding pool safety, the majority of which includes a requirement for a safety fence around the perimeter of the top of an in-ground pool. If a rectangular in-ground pool has a length that is $2$ feet less than twice its width, and the area of the top of the pool is $480$ square feet, how many linear feet of fencing are required, assuming the fence is placed $1$ foot from the edge of the water on all sides?

• A. $92$
• B. $100$
• C. $108$
• D. $116$

Answer 1

Answer: (B)

$100$

Solution:

Given that:

Area of the top of the pool$=480ft{.}^2$

To find:

Number of linear feet of fencing$=?$

Solution:

Let $l$ be the length and $w$ be the width of the rectangular in-ground pool.

$A/q$

$l=2w-2$

Area of the top of the pool$=480ft{.}^2$

or, $l\times w=480ft{.}^2$

or, $(2w-2)w=480$

or, $w^2-w-240=0$

or, $(w-16)(w+15)=0$

or, $w=16$ or $w=-15$

$\therefore$ Width of the rectangular in-ground $=16ft.$

and Length of the rectangular in-ground $=2\times 16-2=30ft.$

Since fencing is done $1ft.$ from the edge

So, Actual length of fence $=30+2=32ft.$

Actual width of the fence $=16+2=18ft.$

Perimeter of the rectangular in-ground$=2(l+b)=2(32+18)=100ft.$

Therefore, No. of linear feet of fences $=100$

Hence, B is the correct option.