# 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?

Algebra ->  Algebra  -> Surface-area -> 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?      Log On

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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(15746)   (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