SOLUTION: John had a square patio. After expanding the length by 20 ft. and the width by 10 ft. the area was 999 ft^2 What was the perimeter of the original patio?
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Question 475032: John had a square patio. After expanding the length by 20 ft. and the width by 10 ft. the area was 999 ft^2 What was the perimeter of the original patio? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! John had a square patio. After expanding the length by 20 ft. and the width by 10 ft. the area was 999 ft^2
What was the perimeter of the original patio?
:
Let x = the length of one side of the square patio
then
(x+20) = the length of the expanded patio
and
(x+10) = the width of the expanded patio
:
Expanded area
(x+20)(x+10) = 999
FOIL
x^2 + 10x + 20x + 200 = 999
:
x^2 + 30x + 200 - 999 = 0
:
x^2 + 30x - 799 = 0
You can solve this using the quadratic formula, but this will factor to:
(x+47)(x-17) = 0
the positive solution:
x = 17 ft
then
4(17) = 68 ft is the original perimeter of the patio
:
:
Check solution by finding the area of the expanded patio
(17+20)(17+10) =
37 * 27 = 999
