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

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) (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=2491/W, eqn3

Substitute eqn 3 in eqn 1:

---> , cross multiply
---> , divide whole eqn by 2:

By Quadratic, where
Discriminant:
Then,

For Width you got 2 values, W1=53cm; W2=47cm

For Length: Via eqn 3,
, and
L1=47cm; L2=53cm

Check on Perimeter:

We use L2 & W2 on Area:

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

Thank you,
Jojo
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