Question

Find the area of a triangle whose sides are 18 cm, 24 cm, and 30 cm. Also, find the length of altitude corresponding to the largest side of the triangle.

Answer 1

Since the sides of the triangle are 18 cm, 24 cm and 30 cm respectively.

s = `(18 + 24 + 30)/(2)`
  = 36

Hence the area of the triangle is 

A  = `sqrt (s( s - a ) ( s - b ) (s -c ))`

    = `sqrt (36( 36 - 18 ) ( 36 - 24 ) (36 -30 ))`

    = `sqrt (36 xx 18 xx 12 xx 6 )`

    = ` sqrt ( 46656 ) `

    = 216 sq.cm.

Again

A = `1/2 "base" xx "altitude" `

Hence

216 = `1/2 xx 30 xx h`
h = 14.4cm