anonymous 4 years ago 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?

1. Mertsj

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2. Mertsj

Let's use x instead of l x(2x-2)=83 2x^2-2x-83=0

3. anonymous

Ok, do i just use the quadratic formula to solve for x?

4. Mertsj

Yes.

5. anonymous

Ok, thank you!

6. Mertsj

yw

7. anonymous

how would i find the length of the diagonal?

8. Mertsj

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.

9. anonymous

Ok, thanks again!!

10. Mertsj

yw

11. Mertsj

12. anonymous

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

13. Mertsj

No.

14. Mertsj

Hang on

15. anonymous

im sorry my arithmetic was incorrect you do get a positive number its radical 668

16. Mertsj

$x=\frac{2\pm \sqrt{2^{2}-4(2)(-83)}}{2(2)}$

17. anonymous

thank you that's what i ended up with$(2\pm \sqrt{668})/4$