SOLUTION: The length of a rectangle is 3 feet less than twice its width and area of rectangle is 27 ft2. Find the dimension Lenth= Width=

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Question 949571: The length of a rectangle is 3 feet less than twice its width and area of rectangle is 27 ft2. Find the dimension
Lenth=
Width=
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
W=width; L=length=2W-3 ft; A=L*W=27 sq ft
A=L*W Substitute for L
27 sq ft=(2W-3)(W)
27+sq+ft=2W%5E2-3W Subtract 27 from each side
0=2W%5E2-3W-27
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 2W%5E2%2B-3W%2B-27+=+0) has the following solutons:

W%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=%28-3%29%5E2-4%2A2%2A-27=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+225+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+225+%29%29%2F2%5C2+=+4.5
W%5B2%5D+=+%28-%28-3%29-sqrt%28+225+%29%29%2F2%5C2+=+-3

Quadratic expression 2W%5E2%2B-3W%2B-27 can be factored:
2W%5E2%2B-3W%2B-27+=+2%28W-4.5%29%2A%28W--3%29
Again, the answer is: 4.5, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-27+%29

ANSWER 1: W=4.5 ft The width is 4.5 feet.
L=2W-3 ft=2(4.5)-3 ft=9 feet-3 feet=6 feet ANSWER 2: The length is 6 feet.
CHECK:
A=L*W
27 sq ft=(6 ft)(4.5 ft)
27 sq ft=27 sq ft