SOLUTION: A rectangle has an area of 2340 sq.cm.. When the length and width are both increased by 2 cm each, the area is increased by 206 sq. cm. Find the original perimeter.

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Question 1101338: A rectangle has an area of 2340 sq.cm.. When the length and width are both increased by 2 cm each, the area is increased by 206 sq. cm. Find the original perimeter.
Found 2 solutions by josgarithmetic, jorel1380:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Rectangle dimensions x and y

xy=2340
-
%28x%2B2%29%28y%2B2%29-xy=206

xy%2B2y%2B2x%2B4-xy=206
2x%2B2y%2B4=206
x%2By%2B2=103
x%2By=101

-
x%2By=101%2Cxy=2340-----either factorize 2340 and look for combinations that work, or substitute and solve a quadratic equation.

x%28101-x%29=2340
101x-x%5E2-2340
-x%5E2%2B101x-2340=0
x%5E2-101x%2B2340=0

discriminant, 101%5E2-4%2A2340=841=29%5E2
highlight%28x=%28101%2B-+29%29%2F2%29-------------one of these will be 'x' and the other is y.

Dimensions: 36 and 65

Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Let l and w be the width and length of the rectangle, respectively. Then:
lw=2340 and
(l+2)(w+2)=2340+206=2546
So:
l=2340/w
(2340/w +2)(w+2)=2546
2340+4680/w+2w+4=2546
4680/w+2w=202
4680+2w²=202w
2w²-202w+4680=0
w²-101w+2340=0
(w-65)(w-36)=0
w=65 or 36
The width is 36; and the length is 65, making the original perimeter 202cm
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