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  1. #1
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    please solve

    Please solve this question using heron's formula..

    The perimeter of an isosceles triangle is 42cm and its base is (3/2)times each of the equal sides.Find the length of each side of the triangle,area of the triangle and height of the triangle.
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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 perimeter of an isosceles triangle is 42cm and its base is (3/2)times each of the equal sides.Find the length of each side of the triangle,area of the triangle and height of the triangle.
    Let x denote the length of one leg. Then the perimeter of the triangle is:

    p = 42 = x+x+\dfrac32 x~\implies~ x = 12

    That means the triangle has the side length:

    a = 12, b = 12, c = 18 (c is the base)

    1. Calculate the area by Heron's formula:

    The half perimeter is s = 21

    A=\sqrt{21(21-12)(21-12)(21-18)}=\sqrt{5103}=27\cdot \sqrt{7} \approx 71.435...\ cm^2

    2. The height of the trinagle. Actually there are (normally) three heights in every triangle. Here 2 of the three heights are equal.

    From A=\dfrac12 \cdot side \cdot height_{side} you get

    h = \dfrac{2A}{side}

    Plug in the values you know to calculate the heights:

    h_{base} = \dfrac{2 \cdot 27\sqrt{7}}{18}=3 \sqrt{7}

    h_{leg} = \dfrac{2 \cdot 27\sqrt{7}}{12}= \dfrac92 \sqrt{7}
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  3. #3
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    i agree with the x=12,x=12,b=18...the h goes through the middle of b
    so to get h..you have to take half of b and one side of the triangle and use pytagore

    12(squared)=9(squared)+h(squared)
    h(squared)=12(squared)-9(squared)
    h(squared)=144-81
    h(squared)=63
    h=3(square root)7
    to get the area b*h/2
    18*3(squared root)7/2
    =54(squared root)7/2
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