SOLUTION: The width of a rectangle is 3 less than twice its length. If the area of the rectangle is 87 cm^2, what is the length of the diagonal?

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Question 962483: The width of a rectangle is 3 less than twice its length. If the area of the rectangle is 87 cm^2, what is the length of the diagonal?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w=-3+2L and wL=87 using w for width and L for length. The question is to find sqrt%28w%5E2%2BL%5E2%29.


L%282L-3%29=87
2L%5E2-3L-87=0
L=%283%2B-+sqrt%289%2B4%2A2%2A87%29%29%2F%284%29
L=%283%2B-+sqrt%28705%29%29%2F4

That discriminant is 15*47, so no further simplifications.


L=%283%2Bsqrt%28705%29%29%2F4

Your choice if you want to handle everything in radical form or to put into decimal base-ten number form. You want something like or equivalent to
w=%283%2Bsqrt%28705%29%29%2F2-3
and then
sqrt%28%28%283%2Bsqrt%28705%29%29%2F2-3%29%5E2%2B%28%283%2Bsqrt%28705%29%29%2F4%29%5E2+%29
Decimalized base-ten form would be easier.