SOLUTION: A rectangular is 8 feetlong 6 feet wide. if each side increased by the same amount,x,the area ofthe new rectangle is 120 square feet. find length and width of the new rectangle

Algebra ->  Test -> SOLUTION: A rectangular is 8 feetlong 6 feet wide. if each side increased by the same amount,x,the area ofthe new rectangle is 120 square feet. find length and width of the new rectangle      Log On


   

Question 18686: A rectangular is 8 feetlong 6 feet wide. if each side increased by the same
amount,x,the area ofthe new rectangle is 120 square feet. find length and width of the new rectangle
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a rectangle:
A+=+LW
The new length is (8+x) ft. and the new width is (6+x) ft. The new area is:
A+=+%288%2Bx%29%286%2Bx%29 = 120 ft^2
%288%2Bx%29%286%2Bx%29+=+120 Perform the indicated multiplication.
48+%2B+14x+%2B+x%5E2+=+120 Rewite in standard form.
x%5E2+%2B+14x+-+72+=+0Solve by factoring.
%28x+-+4%29%28x+%2B+18%29+=+0 Apply the zero products principle.
x+-+4+=+0 and/or x+%2B+18+=+0
If x+-+4+=+0, then x+=+4
If x+%2B+18+=+0, then x+=+-18 Discard this solution as not meaningful because the new length and width cannot be negative.
The new length is: 8+%2B+4+=+12 ft.
The new width is: 6+%2B+4+=+10 ft.
Check:
The new area is 120 ft^2
A+=+%2812%29%2810%29 = 120 ft.^2