Question

A pool measuring 14 meters by 28 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combined is 1176 square​ meters, what is the width of the​ path?

Answer 1

Let's call the width of the path "x". The dimensions of the pool plus the path will be 14+2x by 28+2x.

The total area of the pool plus the path can be found by multiplying the length and width together:

(14+2x) * (28+2x) = 1176

Expanding the brackets, we get:

392 + 56x + 28x + 4x^2 = 1176

Simplifying, we get:

4x^2 + 84x - 784 = 0

Dividing both sides by 4, we get:

x^2 + 21x - 196 = 0

This is a quadratic equation, which can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = 21, and c = -196. Plugging these values into the formula gives:

x = (-21 ± sqrt(21^2 - 4(1)(-196))) / 2(1)

x = (-21 ± sqrt(1681)) / 2

x = (-21 ± 41) / 2

The positive solution is:

x = (-21 + 41) / 2

x = 10/2

x = 5

Therefore, the width of the path is 5 meters.