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anonymous

  • 4 years ago

The difference between the length of the hypotenuse and the length of the next longest side of a right triangle is 3 cm. The difference between the lengths of the two perpendicular sides is 3 cm. Find the three side lengths.

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  1. anonymous
    • 4 years ago
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    I don't get it..

  2. TuringTest
    • 4 years ago
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    call the hypotenuse length x:|dw:1329352306450:dw|use the Pythagorean theorem:\[x^2=(x-3)^2+(x-6)^2\]and solve for x.

  3. anonymous
    • 4 years ago
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    why is it x-3, and x-6?

  4. anonymous
    • 4 years ago
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    as The difference between the lengths of the two perpendicular sides is 3 cm

  5. anonymous
    • 4 years ago
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    So once I get: \[(x ^{2}-6x+9)(x ^{2}-12x+36)\]

  6. anonymous
    • 4 years ago
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    what do I do after?

  7. anonymous
    • 4 years ago
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    utzz...rong u r missin +sign in between

  8. anonymous
    • 4 years ago
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    \[(x ^{2}-6x+9)+(x ^{2}-12x+36)=x ^{3}\]

  9. anonymous
    • 4 years ago
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    ohh, yup I put that now. And so I add to: 2x^2 - 18x + 45?

  10. anonymous
    • 4 years ago
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    imean....x^2

  11. anonymous
    • 4 years ago
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    equate to x^2

  12. anonymous
    • 4 years ago
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    huh?

  13. anonymous
    • 4 years ago
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    so the equation becomes....... 2x^2 - 18x + 45=x^2

  14. anonymous
    • 4 years ago
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    hence 2x^2 - 18x + 45-x^2=0

  15. anonymous
    • 4 years ago
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    x^2 - 18x + 45?

  16. anonymous
    • 4 years ago
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    x^2 - 18x + 45=0

  17. anonymous
    • 4 years ago
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    => (x-3)(x-15)=0

  18. anonymous
    • 4 years ago
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    hence x=3 or x=15

  19. anonymous
    • 4 years ago
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    got it?/

  20. TuringTest
    • 4 years ago
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    ...and since x=3 will not produce a triangle we have x=15

  21. anonymous
    • 4 years ago
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    yeah right...

  22. anonymous
    • 4 years ago
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    ohh..

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