Answer: The width of the pool is 24m and the length of the pool is 29m
Step-by-step explanation: The dimensions of the rectangular pool is not given, but the clues we have are that the length of the pool is 5 meters longer than it’s width. With that information, we can say that the width is W, while the length is W + 5.
Also the pool is surrounded by a walk 4m wide. That means the total length including the two walkways is W + 5 + 4 + 4 (that equals W + 13), and the total width including the two walkways is W + 4 + 4 (that equals W + 8). We have yet another clue, which states that the total area of the pool and walk is 488m more than the area of the pool.
We shall label the area of the pool as AP. If Area = L x W, then area of pool is
AP = (W + 5) x W
AP = W^2 + 5W
Also the total area of the pool and walk shall be labeled as APW. Therefore,
APW = (W + 13) x (W + 8)
APW = W^2 + 8W + 13W + 104
APW = W^2 + 21W + 104
Having calculated the area of the pool as W^2 + 5W and the total area of the pool and walk as W^2 + 21W + 104, and remembering that the area of pool and walk is 488 meters more than the area of the pool, we can now write the following equation;
W^2 + 21W + 104 = W^2 + 5W + 488
Collecting like terms we now have
W^2 - W^2 + 21W - 5W = 488 - 104
16W = 384
Divide both sides of the equation by 16
W = 24.
If the length of the pool has been given as 5 meters more than its width, then length of the pool equals 24 + 5 and that equals 29 meters. Therefore
Length = 29m and Width = 24m
