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You just had a pool installed that has dimensions 10 feet by 24 feet by 4 feet. You want to install a cement patio all the way
around the pool that extends the same distance around every side of the pool. A cement truck holds enough cement to cover
810 square feet at a 4-inch depth. If you don't want to have to pay for a second truck,
what is the widest you can make the patio around your new pool?
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The outer dimensions of the patio are (10+2x) feet wide and (24+2x) feet long.
The area of this rectangle is (10+2x)*(24+2x) square feet.
The area of the pool surface (which obviously is not covered by cement) is 24*10 square feet.
The difference of the areas is the area of the cement patio all the way around the pool. So, this area is
(10+2x)*(24+2x) - 10*24 = = .
So your equation is
= ,
= 0,
= = .
The only positive root is x = = 8.1 ft.
Answer. The width of the patio is approximately 8.1 ft all the way around the pool.
Check. (10+2*8.1)*(24+2*8.1) - 10*24 = 813.24 ft^2 which is close enough.
The solution by "josgaritmetic" is a) and b) starting from his very first equation.
For many other similar solved problems see the lessons
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Problems on a circular pool and a walkway around it
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".