SOLUTION: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 183 cm^2, what is the length of the diagonal?
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Question 204198: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 183 cm^2, what is the length of the diagonal?
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Let the length of the rectangle be L
Since its width is 4 less than twice its length, then width = 2L - 4
Since its area = 183 cm^2, then we’’ll have:
L(2L – 4) = 183
Using the quadratic equation: , where:
a = 2 ; b = - 4 ; c = - 183, we have:
or
or
L = or
Since we CANNOT have a negative measurement, we reject L = - 8.62
Therefore, the length (or base) of the rectangle is 10.62 cm, and the width (or height) = 2(10.62) – 4 = 21.24 – 4 = 17.24 cm.
To now find the diagonal, we use the Pythagorean formula: , using the length and width as “a” & “b” and the diagonal as “c.”
c, or the diagonal = cm.
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