SOLUTION: The area of a rectangular piece of cardboard is 1155. Its perimeter is 136. What is the length and the width.

Since the perimeter is 136 units, half of the perimeter is 68 units.

Let x be the length.  Then the width is (68-x) units.


Equation for the area is length*width = 1155, or

    x*(68-x) = 1155.


Simplify to the standard form quadratic equation

    68x - x^2 = 1155

    x^2 - 68x - 1155 = 0.


Use the quadratic formula to find the roots

     =  =  = .


There are two roots, 35 and 33.

It gives 35 for the length (which is longer) and 68-35 = 33 for the width (which is shorter).


At this point, the problem is just solved in full.


ANSWER.  The length is 35 units.  The width is 33 units.