SOLUTION: The length of a rectangle is 5 meters longer than the width. If the area is 22 square meters, find the rectangle's dimensions.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The length of a rectangle is 5 meters longer than the width. If the area is 22 square meters, find the rectangle's dimensions.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 955277: The length of a rectangle is 5 meters longer than the width. If the area is 22 square meters, find the rectangle's dimensions.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
W=width; L=length=W+5m
A=L*W Substitute for L.
22m%5E2=%28W%2B5m%29W
22m%5E2=W%5E2%2B5Wm Subtract 22m^2 from each side.
0=W%5E2%2B5Wm-22m%5E2
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 1W%5E2%2B5W%2B-22+=+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=%285%29%5E2-4%2A1%2A-22=113.

Discriminant d=113 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+113+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%285%29%2Bsqrt%28+113+%29%29%2F2%5C1+=+2.81507290636732
W%5B2%5D+=+%28-%285%29-sqrt%28+113+%29%29%2F2%5C1+=+-7.81507290636732

Quadratic expression 1W%5E2%2B5W%2B-22 can be factored:
1W%5E2%2B5W%2B-22+=+1%28W-2.81507290636732%29%2A%28W--7.81507290636732%29
Again, the answer is: 2.81507290636732, -7.81507290636732. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-22+%29

W=2.815m ANSWER 1: The width is 2.815 meters.
L=7.815m ANSWER 2: The length is 7.815 meters.
CHECK:
A=L*W
22m%5E2=%287.815m%29%282.815m%29
22m%5E2=21.999m%5E2