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? If x represents the width of the patio, then which of the following equations could be used to solve the word problem?

Answer 1

Area of pool part = Area of large rectangle - Area of the pool

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

2400 = Area of large rectangle - 2400

Area of massive 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 period of the pool, wherein x is the distance from the pool facet to the patio area.

We also want the width of the huge 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

zero = 4[x² + 50x - 600]

0 = x² + 50x - 600

zero = [x - 60] [x + 10]

x - 60 = 0 OR x + 10 = zero

x = 60 OR x = -10

We can only use the positive price of x for the reason that context is duration.

x = 60

Answer 2

the complete question in the attached figure

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

we know that
area of the pool=40*60-----> 2400 ft²

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