A triangle has sides `35 cm, 54 cm` and `61 cm` long. Find its area. Also, find the smallest of its altitudes.

Explanation

`s=(a+b+c)/2=(35+54+61)/2=75`

`/_=sqrt(s(s-a)(s-b)(s-c)`

`/_=sqrt(75(75-35)(75-54)(75-61)`

`=sqrt(75*40*21*14)`

`=420sqrt5cm^2`

`/_=1/2*b*h`

`1/2*61*(h)=420sqrt5`

`h=(420*2sqrt5)/61`

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