## 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, what is the length of the diagonal? Are the two sides x and 2x-2, then multiply them together and equate it to 83. Then solve using quadratic equ. Finally plug it in and use the pythagorean to get the diagonal? Are these the correct steps?

1. anonymous

hey mertsj i think you were helping me with it last week, cant seem to get the correct answer

2. Mertsj

|dw:1328323339784:dw|

3. Mertsj

$x(2x-2)=83$ $2x^2-2x-83=0$

4. anonymous

yea thats what i get so i disregard the negative solution after using the quad equ. and plug my x back into the x and 2x-2 right?

5. Mertsj

Yes those are the correct steps. Are you absolutely certain you have the area right. It is such a weird number and makes the polynomial unfactorable.

6. anonymous

yea thats what the problem says, ive been doing it like everyday for the past week and keep getting something wrong

7. Mertsj

Well double check once again. And I will work through it. We can see if we agree.

8. anonymous

ok

9. anonymous

It is factorable using the quadratic equation

10. Mertsj

So I got the diagonal is 13.80 in decimal form. I will work it out in exact radical form as well.

11. anonymous

how did you get the 13.80 because im getting something else. is it $(2+^{\sqrt{668}})/4$ for x

12. Mertsj

Well if the Great Satellite is here, he is undoubtedly correct. I will check my calculations.

13. anonymous

for x i get $\frac{1+\sqrt{167}}{2}$ (via wolfram) and then $2x-2=1+\sqrt{167}-2=-1+\sqrt{167}$ then again using wolfram i squared and took the square root, but i repeat i make no claim that it is right

14. anonymous

do you know what the full decimal on that 15.46 answer is b/c i plugged it in and it says its wrong, however sometimes it requires that i write out the entire decimal

15. anonymous

I'm getting around 13.8064 as well

16. anonymous

yes i am wrong, mertsj (also quite great i would say) is right

17. anonymous

yes i am as well im going to try it once more and see if i can get another answer

18. anonymous
19. anonymous

The full radical is: $\frac{\sqrt{-6\sqrt{167}-140}}{2}$

20. anonymous

ok, it finally took my answer. it was 13.8064 trick was i wasn't able to round it to 13.8

21. anonymous

thank you everybody, i really appreciate the help