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

Explanation

Let say sides be `a=35cm,b=54 and c=61cm`
`s=1/2(a+b+c)`
`=1/2(35+54+61)`
`=150/2=75cm`
Area of triangle`=sqrt(s(s−a)(s−b)(s−c))`
`=sqrt(75(75−35)(75−54)(75−61))`
`=sqrt(75xx40xx21xx14)`
`=sqrt(25×3×4×10×7×3×7×2)`
`=sqrt(5xx5xx3xx3xx2xx2xx7xx7xx2xx2xx5)`
`=5xx3xx2xx7xx2xxsqrt5`
`=939.15cm^2`
Smallest altitude will be the altitude on greatest side
So, Area of triangle`=939.15`
`1/2xx61xxh=939.15`
`h=30.8cm`(approx).