SOLUTION: the area of a rectangle is 56 and its perimeter is 30. find the difference of its length and width

Question 845367: the area of a rectangle is 56 and its perimeter is 30. find the difference of its length and width
Found 2 solutions by josgarithmetic, hamsanash1981@gmail.com:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x and y are the dimensions, one of them length and the other width.

Area description means xy=56 and perimeter description means 2x+2y=30. For just solving the problem asked, solving for x and y is more important and would be done first.

The perimeter equation is easily simplified to x+y=15. This also directly gives y=15-x and can be substituted....

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Easily mentally skipping steps, the difference between the length and width is ONE UNIT.
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In case one could not skip the steps, then continuing form the factored quadratic equation, either x=7 or x=8.
Using area equation xy=56, find that y=56/x.
That means either y=56/7=8 or y=56/8=7.
Either way, the difference between x and y is 1.
Answer by hamsanash1981@gmail.com(151) (Show Source): You can put this solution on YOUR website!
area = 56
l*b = 56
perimeter = 30
2(l+b) = 30
l+b = 15
squaring on both sides
(l+b)^2 = 225

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