SOLUTION: a rectangle has a perimeter of 12.0 meters. The area of the rectangle is 61.0 percent of maximum area for a rectangle with this perimeter. What is the length of the shorter side?

Question 255004: a rectangle has a perimeter of 12.0 meters. The area of the rectangle is 61.0 percent of maximum area for a rectangle with this perimeter. What is the length of the shorter side?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a rectangle has a perimeter of 12.0 meters.
The area of the rectangle is 61.0 percent of maximum area for a rectangle with this perimeter.
What is the length of the shorter side?
:
Max area is when the rectangle is square, in this case 3*3 = 9 sq/m
:
.61 * 9 = 5.49 sq/m
:
Let L = length, x = the width
2L + 2x = 12
Simplify
L + x = 6
L = (6-x)
:
The area:
x(6-x) = 5.49
6x - x^2 = 5.49
A quadratic equation
-x^2 + 6x - 5.49 = 0
Solve this using the quadratic equation, you should get two solutions
x = 4.87
x = 1.13 m is the shorter side
;
:
Check this by finding the area
4.87 * 1.13 = 5.50 ~ 5.49
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