A rectangular pool is surrounded by a walk 2 meters wide.

Question

A rectangular pool is surrounded by a walk 2 meters wide. The pool is 5 meters longer than its width. If the total area of the pool and walk is 172 square meters more than the area of the​ pool, find the dimensions of the pool.

Answer 1

Hi Kate,

1. Let the width of the pool be w meters.
2. The pool is 5 meters longer than its width, so the length is w + 5 meters.
3. The width of the area including the walk is w + 4 meters.
4. The length of the area including the walk is w + 9 meters.
5. The area of just the pool is w * (w + 5).
6. The total area including the walk is (w + 4) * (w + 9).
7. This total area is 172 square meters more than the pool's area.

To find the dimensions, solve the equation: (w + 4) * (w + 9) = w * (w + 5) + 172

After solving, the width of the pool is 17 meters and the length is 22 meters.

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Best,

Ben

Answer 2

l = w + 5

Area of pool = l × w = (w+5) × w = w² + 5w

The sidewalk adds two to each side of the pool, or a total of four more to the length and the width.

Area of pool plus sidewalk = ((w+5)+4)×(w+4) =

(w+9)×(w+4) = w² + 13w + 36

Area of pool plus sidewalk minus area of pool

= (w² +13w + 36) - (w² + 5w) = 8w + 36 = 172

Subtract 36 from both sides:

8w = 136

DIvide both sides by 8:

w = 17

So, the width is 17 meters and the length is 22 meters.

The area of the pool is 374 square meters.

The area of the pool and its surrounding sidewalk is 21 meters by 26 meters, or 546 square meters.

546 - 374 = 172 square meters, which checks out.