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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.
Solution
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
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