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25 August, 17:14

Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles. This is a triangle. side a has a length of 12 yards. side b has a length of 20 yards. side c has a length of 28 yards. The altitude to side c has a length of X yards.

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  1. 25 August, 17:17
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    Step-by-step answer:

    The area of a triangle with given sides 12,20 and 28 yards can be found using Hero's formula:

    s = (12+20+28) / 2=30

    Area=sqrt (s (s-12) (s-20) (s-28))

    =sqrt (30*18*12*2)

    =sqrt (36^2*10)

    =36sqrt (10)

    Using the standard formula for area of triangle

    Area = (base) (height) / 2

    =28*height/2

    =14*height

    Since the two methods must produce the same area, we can equate the two values to get

    36sqrt (10) = 14*height

    which when simplified gives

    height

    =36sqrt (10) / 14

    = 18sqrt (10) / 7

    = 8.1 yards (to 1 decimal place)
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