SOLUTION: The perimeter of a rectangle is 46 inches and the area is 76 in. squared. What is the length of the shorter sides? I have attempted to solve but keep getting negative numbers.

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Question 783929: The perimeter of a rectangle is 46 inches and the area is 76 in. squared. What is the length of the shorter sides?

I have attempted to solve but keep getting negative numbers.
L=longer side; W=shorter side
46= 2L+2W
46-2W=2L
23-w=l
76=L x W
76= (23-W) x W --> multiply by W
=23w-w^2 --> divide by W
= 23-W
76-23= -w
53= -w
-53=w

Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website!
area of rectangle = length * breadth
76 = l * b
l = 76/b
Perimeter = 2*length + 2*breadth
46 = 2l + 2b
Substitute l = 76/b
46 = 2(76/b) + 2b
46 = 152/b + 2b
Common denominator = b
46b = 152 + 2b^2
Sort into equation
2b^2 - 46b + 152 = 0
Divide by 2
b^2 - 23b + 76 = 0
(b - 4)(b - 19) = 0
b = either 4 or 19 inches.
Hope this helps.
:-)