SOLUTION: John and Chris Maney have designed a new in-ground swimming pool for their backyard. The pool is rectangular and measures 30 feet by 20 feet. They have also designed a tile border

Question 399108: John and Chris Maney have designed a new in-ground swimming pool for their backyard. The pool is rectangular and measures 30 feet by 20 feet. They have also designed a tile border to go around the pool. The tile border covers 216 square feet in area. What is the width x of this tile border?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
John and Chris Maney have designed a new in-ground swimming pool for their backyard.
The pool is rectangular and measures 30 feet by 20 feet.
They have also designed a tile border to go around the pool.
The tile border covers 216 square feet in area.
What is the width x of this tile border?
:
Find the area of the pool: 30 * 20 = 600 sq/ft
Find the overall area (A) which includes the border:
(2x+30)(2x+20)
FOIL
A = 4x^2 + 40x + 60x + 600
A = 4x^2 + 100x + 600; the overall area
:
Overall area - pool area = 216
4x^2 + 100x + 600 - 600 = 216
A quadratic equation
4x^2 + 100x - 216 = 0
Simplify, divide by 4
x^2 + 25x - 54 = 0
Factors to:
(x-2)(x+27) = 0
the positive solution
x = 2 ft is the width of the border
:
:
Check this, overall dimensions would be 24 by 34, find the area:
24 * 34 = 816
Subtract the pool area (600) and you have the given area of 216

RELATED QUESTIONS
The Johnson family is installing a round swimming pool in their backyard. Their backyard... (answered by stanbon)

Mr. and Mrs. Lin have a rectangular swimming pool that is 8 feet deep,20feet long, and 14 (answered by ewatrrr)

a rectangle yard measures 50 ft. long and 40 ft wide, it contains a rectangular swimming... (answered by fractalier)

A rectangular swimming pool with dimension of 11 meters and 8 meters is built in a... (answered by ikleyn)

A rectangular swimming pool with dimensions of 11m and 8m is built in a rectangular... (answered by mananth)

i need to write an equation for the word problem: To estimate the number of people in... (answered by rothauserc)

Henry just installed a new rectangular pool in his backyard. The length of the pool is 24 (answered by farbonara)

A celebrity couple wants to have a rectangular pool put in the backyard of their vacation (answered by JulietG)

A celebrity couple wants to have a rectangular pool put in the backyard of their vacation (answered by solver91311)