Question

the three sides of a triangle are 26 cm and 30 cm. Find the height corresponding to the longest side​

Answer 1

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.