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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?

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  1. anonymous
    • 4 years ago
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    hey mertsj i think you were helping me with it last week, cant seem to get the correct answer

  2. Mertsj
    • 4 years ago
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    |dw:1328323339784:dw|

  3. Mertsj
    • 4 years ago
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    \[x(2x-2)=83\] \[2x^2-2x-83=0\]

  4. anonymous
    • 4 years ago
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    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
    • 4 years ago
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    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
    • 4 years ago
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    yea thats what the problem says, ive been doing it like everyday for the past week and keep getting something wrong

  7. Mertsj
    • 4 years ago
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    Well double check once again. And I will work through it. We can see if we agree.

  8. anonymous
    • 4 years ago
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    ok

  9. anonymous
    • 4 years ago
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    It is factorable using the quadratic equation

  10. Mertsj
    • 4 years ago
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    So I got the diagonal is 13.80 in decimal form. I will work it out in exact radical form as well.

  11. anonymous
    • 4 years ago
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    how did you get the 13.80 because im getting something else. is it \[(2+^{\sqrt{668}})/4\] for x

  12. Mertsj
    • 4 years ago
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    Well if the Great Satellite is here, he is undoubtedly correct. I will check my calculations.

  13. anonymous
    • 4 years ago
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    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
    • 4 years ago
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    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
    • 4 years ago
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    I'm getting around 13.8064 as well

  16. anonymous
    • 4 years ago
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    yes i am wrong, mertsj (also quite great i would say) is right

  17. anonymous
    • 4 years ago
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    yes i am as well im going to try it once more and see if i can get another answer

  18. anonymous
    • 4 years ago
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    The full radical is: \[\frac{\sqrt{-6\sqrt{167}-140}}{2}\]

  19. anonymous
    • 4 years ago
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    ok, it finally took my answer. it was 13.8064 trick was i wasn't able to round it to 13.8

  20. anonymous
    • 4 years ago
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    thank you everybody, i really appreciate the help

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