SOLUTION: Please help me in this question!! The perimeter of a rectangle is 54 centimeters, and it's area is 140 square centimeters. Find the dimensions of the rectangle.

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Question 954600: Please help me in this question!!
The perimeter of a rectangle is 54 centimeters, and it's area is 140 square centimeters. Find the dimensions of the rectangle.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
P=2(L+W)
54cm=2(L+W)
27cm=L+W
27cm-W=L
A=L*W
140cm%5E2=L%2AW Substitute for L.
140cm%5E2=%2827cm-W%29W
140cm%5E2=27Wcm-W%5E2
W%5E2-27W%2B140=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 1W%5E2%2B-27W%2B140+=+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=%28-27%29%5E2-4%2A1%2A140=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+169+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+20
W%5B2%5D+=+%28-%28-27%29-sqrt%28+169+%29%29%2F2%5C1+=+7

Quadratic expression 1W%5E2%2B-27W%2B140 can be factored:
1W%5E2%2B-27W%2B140+=+1%28W-20%29%2A%28W-7%29
Again, the answer is: 20, 7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-27%2Ax%2B140+%29

W=7cm
ANSWER:The width is 7cm.
L=27cm-W=20 cm ANSWER 2: The length is 20 cm.
CHECK:
A=L*W
140cm%5E2=20cm%2A7cm
140cm%5E2=140cm%5E2
.
P=2(L+W)
54cm=2(20cm+7cm)
54cm=2(27cm)
54cm=54cm