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24.07.2022 - 21:07

A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.

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A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.

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Twyla April 16, 2023 в 03:11

Let x be the width of the pool. Then the length of the pool is 2x since it is twice as long as it is wide. The width of the pool and the walkway combined is x + 4 since the walkway is 2 feet wide on each side. The length of the pool and the walkway combined is 2x + 4. The area of the pool and the walkway combined is (x + 4)(2x + 4). The area of just the walkway is given as 196 square feet. So we can write: (x + 4)(2x + 4) - x(2x) = 196 Simplifying the left side: 2x^2 + 12x + 16 - 2x^2 = 196 12x + 16 = 196 12x = 180 x = 15 So the width of the pool is 15 feet and the length of the pool is 30 feet (twice the width).

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