SOLUTION: what is the dimensions of a rectangle that has a perimeter of 56 and an area of 96?

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Question 254777: what is the dimensions of a rectangle that has a perimeter of 56 and an area of 96?
Answer by palanisamy(496) About Me  (Show Source):
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Let a and b be the two sides of a rectangle
Then perimeter 2(a+b) = 56
(a+b) =28 ..(1)
Area ab = 96 ...(2)
Next, (a-b)^2 = (a+b)^2-4ab
=(28)^2-4*(96)
= 784-384
(a-b)^2 = 400
a-b = 20 ...(3)
(1)+(3)=> 2a = 28+20
2a = 48
a = 24
Substituting in (1),
24+b = 28
b = 28-24
b = 4
Therefore the sides are 24 and 4