Dimension of the pool

A rectangular pool is surrounded by a walk 4 feet wide. The pool is 6 feet longer that it is wide. If the area of the pool and the walk is 272 square feet more than the area of the pool. What are the dimensions of the pool?


I really dont get the right answer :( , please help me to understand this. I need the solution

Expert Answers

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You need to use the following notation for the length and the width of the pool: L and w

Since the problem provides the information that the pool is 6  feet longer than its wide, hence L = 6+w.

You need to evaluate the area of the pool:

A_p = L*w => A_p = (6+w)*w

The problem provides the information that the pool is surounded by a walk of 4 ft wide, hence the dimensions of pool and walk are: length = 8+L and width = 8+w

A_w = (8+L)(8+w) => A_w = (8+6+w)(8+w) =>A_w = (14+w)(8+w)

Since area of pool and walk is 272 sq feet more than area of pool, then you may write such that:

 (14+w)(8+w) = 272+(6+w)*w

You need to open the brackets such that:

112 + 22w + w^2 - 272 - 6w - w^2 = 0

16w-160 = 0 => 16w = 160 => w = 10 feet

L = 6+w => L = 10+ 6=> L = 16 feet

Hence, evaluating the dimensions of pool yields the length of 16 feet and the width of 10 feet.

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