SOLUTION: If the perimeter of a rectangle is 46 cm and the area is 120 square cm, then what are the dimensions of the rectangle? The width, or shorter side is The length, or longer side

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: If the perimeter of a rectangle is 46 cm and the area is 120 square cm, then what are the dimensions of the rectangle? The width, or shorter side is The length, or longer side      Log On


   

Question 1027866: If the perimeter of a rectangle is 46 cm and the area is 120 square cm, then what are the dimensions of the rectangle?
The width, or shorter side is
The length, or longer side is
Answer by ikleyn(52781) About Me  (Show Source):
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If the perimeter of a rectangle is 46 cm and the area is 120 square cm, then what are the dimensions of the rectangle?
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Let x be the length and y be the width.

Then 

x + y =  23,   (1)     ( 23 = 46%2F2 )
xy    = 120.   (2)

Express x = 23 - y from (1) and substitute into (2). You will get

(23-y)*y = 120.

Solve this quadratic equation:

23y+-+y%5E2 = 120,

y%5E2+-+23y+%2B+120 = 0.

Factor the left side:

(x - 15)*(x-8) = 0.

The roots are 8 and 15.

The width, or shorter side is   8 cm.
The length, or longer side is  15 cm.