A rectangle swimming pool is 24m longer than it is wide and is surrounded by a deck 3m wide. Find the area of the pool if the area of the deck is 324m2. Where do I even start to solve this problem?
Before you dive right in and begin calculating, it's best to take a look at what information you were given and what you already know. You're told that the pool's length is equal to the width plus 24, or l = w + 24. And since you know that the area of a rectangle is equal to its length times its width, then the pool's area is
(w + 24) x w
or
w2 + 24w
You also know you're essentially dealing with two rectangles — one rectangle is the pool and the other is the big rectangle that includes the pool plus the deck. So it makes sense that if you subtract the deck area, which you're told is 324m2, from the pool plus deck area, you'll end up with the area of the pool.
To find the area of the big rectangle (pool plus deck), you need to account for the 3m deck around the pool. That means the big rectangle's width would be the pool's width plus the deck's width on both sides: w + 3 + 3 or w + 6
In the same way, the 3m deck is on both sides of the pool's length, so the big rectangle's length would be w + 24 + 3 + 3 or w + 30
So the area of the pool plus the deck is
(w + 6) X (w + 30)
or
w2 + 36w + 180
Now you have all you need to solve the problem:
Area of pool = (Area of pool plus deck) – (Area of deck)
w2 + 24w = (w2 + 36w + 180) - 324
Solve for w to find the width of the pool:
w2 + 36w +180 - w2 - 24w = 324
12w + 180 = 324
12w = 144
w = 12
If the pool's width is 12, then the pool's length should be 12 + 24, and you can find the pool's area:
Area of pool = 12 x 36
Area of pool = 432 m2