SOLUTION: the length of a rectangle is 2 more than twice its width. if the area of the rectangle is 24 square meters, find its dimension

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Question 950670: the length of a rectangle is 2 more than twice its width. if the area of the rectangle is 24 square meters, find its dimension
Found 2 solutions by macston, Gogonati:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
W=width; L=length=2W+2; A=area=L*W=24 sq m
A=L*W Substitute for L
24 sq m=(2W+2)(W)
24+sq+m=2W%5E2%2B2W Subtract 24 sq m from each side
0=2W%5E2%2B2W-24+sq+m
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 2W%5E2%2B2W%2B-24+=+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=%282%29%5E2-4%2A2%2A-24=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+196+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%282%29%2Bsqrt%28+196+%29%29%2F2%5C2+=+3
W%5B2%5D+=+%28-%282%29-sqrt%28+196+%29%29%2F2%5C2+=+-4

Quadratic expression 2W%5E2%2B2W%2B-24 can be factored:
2W%5E2%2B2W%2B-24+=+2%28W-3%29%2A%28W--4%29
Again, the answer is: 3, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-24+%29

W=3 ANSWER 1: The width is 3 meters.
L=2W+2=2(3m)+2=6m+2m=8m ANSWER 2: Length is 2 meters.
CHECK:
Area=L*W=24 sq m
8m*3m=24 sq m
24 sq m=24 sq m

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width be x m, than the length will be 2x+2 m. The area of the rectangle will be: x(2x+2)=24. Solving this quadratic equation we get:
x^2+ x-12=0
(x+4)(x-3)=0
{-4, 3}
Since the dimension is always positive, the width of the rectangle is 3 m, and the length is 8m.