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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.
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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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