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Question
Find the area of the triangle whose sides are 18 cm, 24 cm and 30 cm. Also find the height corresponding to the smallest side.
Solution
Let the sides of triangle be a=18 cm, b=24 cm and c=30 cm
Let s be the semi-perimeter of the triangle.
s=`1/2(a+b+c)`
s=`1/2(18+24+30)`
s=`36 cm`
Area of a triangle = `sqrt(s(s-a)(s-b)(s-c))`
=`sqrt(36(36-18)(36-24)(36-30))`
=`sqrt(36xx18xx12xx6)`
=`sqrt(46656)`
=`216 cm^2`
The smallest side is 18 cm long. This is the base.
Now, area of a triangle = `1/2xxbxxh`
⇒ `216=1/2xx18xxh`
⇒ `216=9h`
⇒`216/9=h`
⇒` h=24 cm`
The height corresponding to the smallest side is 24 cm
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