SOLUTION: A rectangular swimming pool is twice as long as it is wide. A small decorative walkway surrounds the pool. If the walkway is a constant 2 feet wide and has an area of 196 square fe

Algebra ->  Rectangles -> SOLUTION: A rectangular swimming pool is twice as long as it is wide. A small decorative walkway surrounds the pool. If the walkway is a constant 2 feet wide and has an area of 196 square fe      Log On


   

Question 956252: A rectangular swimming pool is twice as long as it is wide. A small decorative walkway surrounds the pool. If the walkway is a constant 2 feet wide and has an area of 196 square feet, what are the dimensions of the pool?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let w and L be the width and the length of the pool.
Let u be the border width. Given u=2.
Let A be the border area given A=196.
Also given is L=2w.


Pool area is wL.
Border area is %28w%2B2u%29%28L%2B2u%29-wL=A because the value was given.

Simplify the border area equation.
wL%2B2uL%2B2uw%2B4u%5E2-wL=A
2uL%2B2uw%2B4u%5E2=A
4u%5E2%2B2uL%2B2uw-A=0
Use the given described L=2w to substitute,
4u%5E2%2B2u%282w%29%2B2uw-A=0
4u%5E2%2B4uw%2B2uw-A=0
4u%5E2%2B%284u%2B2u%29w-A=0
4u%5E2%2B6uw-A=0
6uw=A-4u%5E2
highlight%28w=%28A-4u%5E2%29%2F6u%29--------Width in a symbolic form result.

Find the value for w.
w=%28196-4%2A2%5E2%29%2F%286%2A2%29
w=%28196-16%29%2F12
w=180%2F12=90%2F6
highlight%28w=15%29---------The value for the width.

Find value for L.
From given L=2w,
highlight%28L=30%29-----------the value for the length.