SOLUTION: The area of a rectangular door is 20 ft. Square.The border around the door is 20 feet. What is the length and width of the door ? Use the factors of 21 to help you find the area of

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Question 956218: The area of a rectangular door is 20 ft. Square.The border around the door is 20 feet. What is the length and width of the door ? Use the factors of 21 to help you find the area of the door first.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
If you mean the door has an area of 20 square feet and perimeter of 20 feet then:
A=area=20 sq ft; P=Perimeter=20 ft; L=length; W=width
P=2%28L%2BW%29
20+ft=2%28L%2BW%29 Divide each side by 2.
10ft=L%2BW
10ft-W=L
A=LW Substitute for L
20ft%5E2=%2810ft-W%29%28W%29
20ft%5E2=10Wft-W%5E2Add W^2-10W to each side.
w%5E2-10W%2B20ft%5E2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-10x%2B20+=+0) has the following solutons:

x%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=%28-10%29%5E2-4%2A1%2A20=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+7.23606797749979
x%5B2%5D+=+%28-%28-10%29-sqrt%28+20+%29%29%2F2%5C1+=+2.76393202250021

Quadratic expression 1x%5E2%2B-10x%2B20 can be factored:
1x%5E2%2B-10x%2B20+=+1%28x-7.23606797749979%29%2A%28x-2.76393202250021%29
Again, the answer is: 7.23606797749979, 2.76393202250021. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B20+%29

W=2.764 ft ANSWER 1: The width is 2.764 feet.
L=10ft-W=10 ft-2.764ft=7.236ft ANSWER 2: The length is 7.236 feet.
CHECK:
A=LW
20ft%5E2=%287.236ft%29%282.764ft%29
20ft%5E2=20ft%5E2
.
-AND-
.
P=2%28L%2BW%29
20ft=2%287.236ft%2B2.764ft%29
20ft=2%2810ft%29
20ft=20ft