Question

A rectangular pool is to be built on a lot that measures 20 m by 12 m. A wooden deck of uniform width, equal to the area of the pool, must surround it. How wide is the strip of the deck? What are the length and width of the pool?

Answer 1

The length and breadth(width) of the pool are

$l\approx15.7m\text{ and }b\approx7.7m$

Let

$l=\text{length of the side of the pool}\\b=\text{breadth of the pool side}\\w=\text{the width of the strip of deck surrounding the pool}$

From the question, we can build the following relationships

$l+2w=20\\b+2w=12$

subtracting to eliminate $w$ (we do not even need it!)

$l-b=8\\b=l-8$

we can also build another relationship from the question. Since the area of the strip equals the area of the pool:

$lb+lb=2lb=20\times 12\\lb=120$

We have two unknowns, $l$ and $b$. Eliminate $b$

$lb=120\\l(l-8)=120\\l^2-8l-120=0$

If we solve the quadratic equation for $l$, we get

$l=4+2\sqrt{34}\approx 15.7m$

and

$b=l-8\\b=(4+2\sqrt{34})-8\\b=2\sqrt{34}-4\approx7.7m$

The length and breadth(width) of the pool are

$l\approx15.7m\text{ and }b\approx7.7m$

Learn more about area here: brainly.com/question/1447350