the three sides of a triangle are 26 cm and 30 cm. Find the height corresponding to the longest side
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By using the Heron's formula,
Area of the triangle = √ s ( s-a) ( s - b) ( s - c)
a = 26 cm
b = 28 cm
c = 30 cm
s = 26 + 28 + 30 / 2
= 42 cm
thus area of the triangle = √ 42 * ( 42 - 26 ) * ( 42 - 28 ) * ( 42 - 30 )
= √ 42 * 16 * 14 * 12
= √ 6*7*4²*2*7*2*6
= 2*4*6*7
= 336 cm²
let the height of the triangle corresponding to the longest side be h cm.
therefore
1/2*h*30 = 336
h = 2*336/30
= 22.4 cm
Thus the height of the triangle corresponding to the longest side is 22.4 cm.
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