Let the length of the rectangle be x then from the Perimeter the sum of the widths will be :
34 - 2x
The length of the width will be :
(34 - 2x)/2 = 17 - x
The area of the rectangle from the measurements will be :
x (17 - x) = 17x - x²
17x - x² = 60
x² - 17x + 60 = 0
Solving for x:
The roots are :
-5 and - 12
x² - 5x - 12x + 60 =0
x(x - 5) - 12 (x- 5) = 0
(x - 5)(x - 12) = 0
x = 5 or 12
We pick 12 since the width should be less than the length.
The width is thus :
17 - 12 = 5cm
Length is : 12cm
