Question

The side of a triangle are 70cm,108cm and 122cm.The length of its longest altitude is:

Answer 1

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$\boxed{ \color{navy} \huge \mathbb{ HOLLA! MATE \: }} \\ \\ \: \: \: \: \: \: \: \: \: \color{blue}\underline{\tt{here \: is \: your \: answer}}$
$\boxed{ \color{navy} \huge \mathbb{ HOLLA! MATE \: }} \\ \\ \: \: \: \: \: \: \: \: \: \color{blue}\underline{\tt{here \: is \: your \: answer}} \\ \\ semiperimeter \: is \: equal \: to \: \\ \frac{(a + b + c)}{2} = \frac{(70 + 108 + 122)}{2} \\ = \frac{300}{2} = 150 \\ the \: heron \: formula \: is \: equal \: to - \\ = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{ 150(150 - 70)(150 - 108)(150 -122 )} \\ = \sqrt{150 \times 80 \times 42 \times 28} \\ \sqrt{14,112,000} \\ = 3,756.60 \\now \: we \: got \: the \: area \: of \: triangle \\ since, \: the \: area \: of \: triangle \: is \: equal \: to \: \\ = \frac{1}{2} \times b \times h \\ hence, \\ 3756.6 = \frac{1}{2} \times 122 \times h \\ 3756.6 = 61 \times h \\ h = \frac{3756.6}{61} = 61.6$

Answer 2

semiperimeterisequalto
(a+b+c)/2
=(70+108+122)​/2
=2300​
=150
using theheronformulaisequalto
=√s(s−a)(s−b)(s−c)​
=√150(150−70)(150−108)(150−122)​
=√150×80×42×28​14,112,000​
=3,756.60
since,the area of triangle is equal to
=1/2×b×h
hence,
3756.6=1/2×122×h
3756.6=61×h
h=3756.6​/61
=61.6​cm

Therefore the length of its longest altitude is 61.6cm