Find shorter side of rectangle?

Question

A rectangle has a perimeter of 14.5 m. The area of the rectangle is 67.0 percent of the maximum area for a rectangle with this perimeter. Calculate the length of the shorter side.

Answer 1

Greetings,

perimeter = 14.5 m

maximum area is that of a square = (14.5/4)^2 = (29/8)^2 = 13.14 m^2

area of rectangle = 67*8.41/64 = 8.8042 m^2

Let the shorter side be s, then the longer side is (14.5 - 2s)/2

and the area = s(7.25 - s) = (67/64)*8.41

s^2 - 7.25s + (67/64)*8.41 = 0

by the quadratic formula

s = (7.25 +/- sqrt(7.25^2 - 4*(67/64)*8.41))/2

s = 1.542596041 or s = 5.707403959

The shorter side is 1.542596041 m

Regards