A rectangle surrounded by another rectangle. Find width of outer rectangle.

Question

The public swimming pool, which is a rectangle measuring 29 meters by 26 meters, needs a new deck. The deck of uniform width that will surround the pool will be made of cement. There is only enough money in the budget to cover 2784 square meters with cement. How wide should the path be?

Answer 1

Draw a figure.

Let x = width of the walk.

The area of the pool is 29 * 26 = 754

The area of the walk and the pool is (29 + 2x)(26 + 2x)

The area of the walk is $754+11x+4x^2-754=2784$

$4x^2+110x-2784=0$

$2x^2+55x-1392=0$

The quadratic formula gives an extraneous root and x = 16