Question

A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around it that is the same width on all sides.If the patio area equals the area of the pool, how wide is the distance from the pool edge to the patio edge?

Answer 1

Area of pool edge = Area of big rectangle - Area of the pool

Area of pool edge = Area of the pool = 40 × 60 = 2400 ft²

2400 = Area of big rectangle - 2400
Area of big rectangle = 2400 + 2400
Area of big rectangle = 4800

Length × width = 4800

From the diagram, we need the length to be [x + x] more than the length of the pool, where x is the distance from the pool edge to the patio edge.

We also need the width of the big rectangle to be [[x + x] more than the width of the pool.

Length = 60 + 2x
Width = 40 + 2x

Length × Width = [60+2x] × [40+2x]
4800 = 2400 + 120x + 80x + 4x²
0 = 4x² + 200x - 2400
0 = 4[x² + 50x - 600]
0 = x² + 50x - 600
0 = [x - 60] [x + 10]

x - 60 = 0 OR x + 10 = 0
x = 60 OR x = -10

We can only use the positive value of x since the context is length

Hence, x = 60

Answer 2

Answer:

Let

x-------> the width of the patio

we understand that

region of the pool=40*60-----> 2400 ft²

vicinity of the patio=[(40+2x)*(60+2x)]-2400

place of the patio=2400 ft²

so

[(40+2x)*(60+2x)]-2400=2400

2400+80x+120x+4x²-4800=0

4x²+200x-2400=0------> divide by 4 both sides----> x²+50x-600=0

therefore

the answer is

x²+50x-600=0