SOLUTION: The width of a rectangle is 8 less than twice its length. If the area of the rectangle is 200 cm^2, what is the length of the diagonal?

Question 341864: The width of a rectangle is 8 less than twice its length. If the area of the rectangle is 200 cm^2, what is the length of the diagonal?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The width of a rectangle is 8 less than twice its length.
If the area of the rectangle is 200 cm^2, what is the length of the diagonal?
:
Let x = the length
then
(2x-8) = the width
and
x(2x-8) = 200; the area
A quadratic equation
2x^2 - 8x - 200 = 0
Simplify, divide by 2
x^2 - 4x - 100 = 0
Find x using the quadratic formula

In this equation: a=1; b=-4; c=-100

The positive solution is what we want here

x =
x = 12.2 is the length
then
2(12.2) - 8 = 16.4 is the width
:
Check solution by finding the area: 12.2 * 16.4 = 200.1 ~ 200, close enough
:
Find the diagonal (d)
d =
c = 20.44 cm is the diagonal

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