SOLUTION: The area of a rectangular door is 20.77 square feet. The width of the door is 3.6 feet more than its length. Find the length and width of the door.

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Question 956703: The area of a rectangular door is 20.77 square feet. The width of the door is 3.6 feet more than its length. Find the length and width of the door.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
L=length; W=width=L+3.6ft; A=area=20.77 sq ft
LW=A Substitute for W
L%28L%2B3.6ft%29=20.77ft%5E2
L%5E2%2B3.6Lft=20.77ft%5E2 Subtract 20.77 sq ft from each side.
L%5E2%2B3.6ftL-20.77ft%5E2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aL%5E2%2BbL%2Bc=0 (in our case 1L%5E2%2B3.6L%2B-20.77+=+0) has the following solutons:

L%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283.6%29%5E2-4%2A1%2A-20.77=96.04.

Discriminant d=96.04 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3.6%2B-sqrt%28+96.04+%29%29%2F2%5Ca.

L%5B1%5D+=+%28-%283.6%29%2Bsqrt%28+96.04+%29%29%2F2%5C1+=+3.1
L%5B2%5D+=+%28-%283.6%29-sqrt%28+96.04+%29%29%2F2%5C1+=+-6.7

Quadratic expression 1L%5E2%2B3.6L%2B-20.77 can be factored:
1L%5E2%2B3.6L%2B-20.77+=+1%28L-3.1%29%2A%28L--6.7%29
Again, the answer is: 3.1, -6.7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3.6%2Ax%2B-20.77+%29

ANSWER 1: The length is 3.1 feet.
W=L+3.6ft=3.1ft+3.6ft=6.7ft
ANSWER 2: The width is 6.7 feet.
CHECK:
LW=A
%283.1ft%29%286.7ft%29=20.77ft%5E2
20.77ft%5E2=20.77ft%5E2