SOLUTION: 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
Algebra ->
Customizable Word Problem Solvers
-> Geometry
-> SOLUTION: 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
Log On
Question 1073062: 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? Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website! .
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.
(