A rectangular swimming pool measures 16 m by 20 m a path of uniform width is built around the pool if the area of the path is 100 m squared find the width of the path giving your answer to correct to 2 decimal place

Answer 1

Let x be the width of the path.

The area of the entire rectangular region, including the pool and the path, is (16 + 2x)(20 + 2x) = 16(20) + 100, since the area of the path is 100 m².

Expanding the left side gives 320 + 72x + 4x² = 320 + 100.

Rearranging gives 4x² + 72x - 100 = 0.

Using the quadratic formula, x = (-72 ± sqrt(72² - 4*4*(-100))) / (2*4).

Calculating gives x = (-72 ± sqrt(8644)) / 8 = (-72 ± 92.894) / 8.

Therefore, x = (-72 + 92.894) / 8 = 20.894 / 8 ≈ 2.61 m.

So, the width of the path is approximately 2.61 m.