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The area of a rectangular piece of cardboard is 1155. Its perimeter is 136.
What is the length and the width.
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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.
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Memorize this method.
Million other similar problems can be solved in this way.