The width of a rectangle is 2 less than twice its length. If the area of the rectangle is 83 cm^2, what is the length of the diagonal? Is there a special diagonal formula?

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The width of a rectangle is 2 less than twice its length. If the area of the rectangle is 83 cm^2, what is the length of the diagonal? Is there a special diagonal formula?

Mathematics
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Let's use x instead of l x(2x-2)=83 2x^2-2x-83=0
Ok, do i just use the quadratic formula to solve for x?

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Yes.
Ok, thank you!
yw
how would i find the length of the diagonal?
After you know x you can find the two sides of the rectangle. Those sides are the legs of a right triangle. The diagonal is the hypotenuse so use the Pythagorean Theorem.
Ok, thanks again!!
yw
It's not a pretty answer.
yea, i can't seem to get x when i plug everything into the quad formula i get an imaginary number because of the negative under the radical
No.
Hang on
im sorry my arithmetic was incorrect you do get a positive number its radical 668
\[x=\frac{2\pm \sqrt{2^{2}-4(2)(-83)}}{2(2)}\]
thank you that's what i ended up with\[(2\pm \sqrt{668})/4\]

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