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.

Answer 1

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