SOLUTION: A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet, but building code laws state that a homeowner cannot have a deck larger than 900

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet, but building code laws state that a homeowner cannot have a deck larger than 900       Log On


   

Question 394940: A homeowner wants to increase the size of a rectangular deck that now measures 15 feet by 20 feet, but building code laws state that a homeowner cannot have a deck larger than 900 square feet. If the length and the width are to be increased by the same amount, find, to the nearest tenth, the maximum number of feet that the length of the deck may be increased in size legally. [Show work.]
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the increase in the number of feet for the width and for the length.
The new area will be:
%2815%2Bx%29%2820%2Bx%29+=+900 Simplify.
300%2B35x%2Bx%5E2+=+900 Rewrite in standard quadratic form.
x%5E2%2B35x-600+=+0 Solve using the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x+=+%28-35%2B-sqrt%2835%5E2-4%281%29%28-600%29%29%29%2F2
x+=+%28-35%2B-sqrt%281225-%28-2400%29%29%29%2F2
x+=+%28-35%2B-sqrt%283625%29%29%2F2
x%5B1%5D+=+-47.6 or x+=+12.6 Discard the negative solution as width/length are positive values.
The length and the width must be increased by 12.6 feet each.