Question

Find the areas of the triangle whose sides are 42 cm, 34 cm and 20 cm. Also, find the height corresponding to the longest side. 

Answer 1

Let the sides of the triangle be a=20cm, b=34 cm  and C= 42cm Let s be the semi-perimeter of the triangle.  

`s=1/2(a+b+c)` 

`s=1/2(20+34+42)` 

`s=48 cm` 

Area of the triangle=`sqrt(s(s-a) (s-b)(s-c))` 

⇒`sqrt(48(48-20)(48-34)(48-42))`

⇒`sqrt(48xx28xx14xx6)` 

⇒`sqrt(112896)` 

⇒`336cm^2 `  

Length of the longest side is 42 cm. 

Area of a triangle =`1/2xxbxxh`   

⇒ `336=1/2xx42xxh` 

⇒` 672=42h` 

⇒`672/42=h` 

⇒`h=16 cm` 

The height corresponding to the longest side is 16 cm.