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  1. #1
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    please solve this question

    please solve this question using heron's formula...

    The lengths of the sides of a triangle are 5cm, 12cm and 13cm.Find the length of perpendicular from the opposite vertex to the side whose length is 13cm.
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  2. #2
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    Quote Originally Posted by rickymylv View Post
    please solve this question using heron's formula...

    The lengths of the sides of a triangle are 5cm, 12cm and 13cm.Find the length of perpendicular from the opposite vertex to the side whose length is 13cm.
    This is a right triangle since 13^2=5^2+12^2

    See diagram:

    The side of 5 is the geometric mean between x and 13.

    \frac{x}{5}=\frac{5}{13}

    13x=25

    x=\frac{25}{13}

    The side 12 is the geometric mean between y and 13.

    \frac{y}{12}=\frac{12}{13}

    13y=144

    x=\frac{144}{13}

    The length of the perpendicular (h) to the hypotenuse is the geometric mean between x and y.

    \frac{\frac{25}{13}}{h}=\frac{h}{\frac{144}{13}}

    Can you finish up.

    Sorry, I misread your instructions. I did not use Heron's formula to solve this.....I'll see if someone else does. Otherwise, I'll be back.

    Okay, I'm back. I really don't know how Heron's formula fits into all this. Heron's formula is a formula for finding the area of any triangle knowing only the lengths of the sides.

    A=\sqrt{s(s-a)(s-b)(s-c)}, where a, b, and c are the sides and s is the semi-perimeter. That is,

    s=\frac{a+b+c}{2}

    The perimeter of your triangle = 5 + 12 + 13 = 30.
    The semi-perimeter (s) = 15
    Substituting into Heron's formula to find Area:

    A=\sqrt{15(15-5)(15-12)(15-13)}=\sqrt{900}=30

    This could just as easily been found using A=\frac{1}{2}bh using b = 12 and h = 5. But, I digress.

    Now, since you just found what the area was, you can use this to solve for your missing perpendicular.

    A=\frac{1}{2}bh

    30=\frac{1}{2}(13)h

    60=13h

    h=\frac{60}{13}

    All done!!
    Attached Thumbnails Attached Thumbnails please solve this question-right.bmp  
    Last edited by masters; October 8th 2008 at 09:01 AM.
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