A man ha s a swimming pool in the form of a square. He constructs a cement walk 6 feet wide around the pool and finds that the area of the walk is exactly one-half the area of the pool. What it the length of the pool?

Let X be the length of the pool.

Area of the pool A1=x^2.

Area of cement walk of 6 ft wide(A2) =(x+12)^2-x^2=x^2+24x+144-x^2

=24x+144.

It is given that A2=A1/2.

24x+144=x^2/2.

x^2-48x-288=0.

By solving using quadratic equation

x=53.4ft.

length of the pool =53.4ft.