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 =...

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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.**