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MBrecht92

  • 2 years ago

The base of a triangle exceeds its height by 17 inches. If its area is 55 square inches, find the base and height of the triangle.

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  1. MBrecht92
    • 2 years ago
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    Hello all.

  2. prettyboy20202
    • 2 years ago
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    sup

  3. MBrecht92
    • 2 years ago
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    Any ideas?

  4. prettyboy20202
    • 2 years ago
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    nope

  5. MBrecht92
    • 2 years ago
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    I thought I should set up the problem this way: 55 = 1/2(h+h+17)

  6. MBrecht92
    • 2 years ago
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    But then I got the wrong answer, as usual

  7. mathstudent55
    • 2 years ago
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    let h = height, then let b = base = h + 17 Area of triangle: A = (bh)/2 55 = (h + 17)h/2

  8. MBrecht92
    • 2 years ago
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    Right, exactly..so 55 = 2h+17/2, and thus h+17/2 = 55. Then, 55*2 = h+17

  9. mathstudent55
    • 2 years ago
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    Your're close, but the formula for the area of a triangle is the base times the height over 2, not the base plus the height over 2.

  10. helder_edwin
    • 2 years ago
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    right \[ \large 55=\frac{(h+17)\cdot h}{2} \]

  11. MBrecht92
    • 2 years ago
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    Um...but I already multiplied the b by the h. It's just that here, b = h + 17

  12. mathstudent55
    • 2 years ago
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    it's not (2h + 17)/2 = 55, it's (h^2 + 17h)/2 = 55

  13. helder_edwin
    • 2 years ago
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    use the distributive law on the denominator

  14. helder_edwin
    • 2 years ago
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    \[ \large 55=\frac{h^2+17h}{2} \]

  15. MBrecht92
    • 2 years ago
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    Okay. So you end up with h^2 + 17h = 110

  16. MBrecht92
    • 2 years ago
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    Then...h^2+17h-110

  17. mathstudent55
    • 2 years ago
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    Right. Now subtract the 110 to the left and solve the quadratic eq.

  18. mathstudent55
    • 2 years ago
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    Set it equal to zero and solve.

  19. MBrecht92
    • 2 years ago
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    (x+22)(x-5) = 0, x = -22, 5

  20. MBrecht92
    • 2 years ago
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    Sorry...I meant h. So h = 5, and then b = (5) + 17 = 22

  21. MBrecht92
    • 2 years ago
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    Thank you for all your help!!

  22. mathstudent55
    • 2 years ago
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    Not x, but h. Now you have h = -22 or h = 5. A negative number is meaningless as the height of a triangle, so dicard it. yes, you got it.

  23. mathstudent55
    • 2 years ago
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    wlcm

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