SOLUTION: Perimeter of a rectangle is 200cm. The Area of the Rectangle is 2491 square cm. what is the size of the rectangle?

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Question 188378: Perimeter of a rectangle is 200cm. The Area of the Rectangle is 2491 square cm. what is the size of the rectangle?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


P=2L+2W= 200cm, eqn1
A=L*W= 2491 sq.cm., eqn2

In eqn 2 we get, L%2Across%28W%29%2Fcross%28W%29=2491%2FW ---> L=2491/W, eqn3

Substitute eqn 3 in eqn 1:
2%28%28highlight%282491%2FW%29%29%29%2B2W=200
4982%2FW%2B2W=200 ---> %284982%2B2W%5E2%29%2FW=200, cross multiply
2W%5E2%2B4982=200W ---> 2W%5E2%2B4982-200W=0, divide whole eqn by 2:
W%5E2-100W%2B2491=0
By Quadratic, wheresystem%28a=1%2Cb=%28-100%29%2Cc=2491%29
Discriminant: b%5E2-4ac=100%5E2-4%281%29%282491%29=10000-9961=red%2836%29
Then,
x=%28-%28100%29%2B-sqrt%2836%29%29%2F%282%2A1%29=100%2B-6%2F2
x=100%2B6%2F2=106%2F2=red%2853%29
x=100-6%2F2=94%2F2=red%2847%29
For Width you got 2 values, W1=53cm; W2=47cm

For Length: Via eqn 3,
L%5B1%5D=2491%2FW%5B1%5D=2491%2F53=red%2847cm%29, and L%5B2%5D=2491%2FW%5B2%5D=2491%2F47=red%2853cm%29
L1=47cm; L2=53cm

Check on Perimeter:
200cm=2%28L%5B1%5D%29%2B2%28W%5B1%5D%29
200cm=2%2847%29%2B2%2853%29
200cm=94cm%2B106cm
200cm=200cm
We use L2 & W2 on Area:
2491cm%5E2=47%2A53
2491cm%5E2=2491cm%5E2

Therefore, Rectangle can be of L1 & W1 or L2 & W2

Thank you,
Jojo