Question

The sides of a triangle are 35cm,54cm,and 61cm respectively. The length of its longest altitude.
a.1675cm
b.1075cm
c.2475cm
d.28cm​

Answer 1

GIVEN:-

• a= 35cm

• B= 54cm

• C= 61cm

TO FIND:-

• Length of it's longest altitude.

FORMULAE USED:-

• ${\boxed{\rm{\sqrt{S(S-a)(s-b)(s-c}}}}$

Where,

S= Perimeter/2

$\implies\rm{S=\dfrac{a+b+c}{2}}$

$\implies\rm{S=\dfrac{35+54+61}{2}}$

$\implies\rm{S=\dfrac{150}{2}}$

$\implies\rm{S=75cm}$

Now, Applying the Formulae

$\implies\tt{Area\:of\:triangle=\sqrt{S(S-a)(S-b)(S-c)}}$

$\implies\tt{\sqrt{(75)(75-35)(75-54)(75-61)}}$

$\implies\tt{\sqrt{75\times{(40)}\times{(21)}\times{(14)}}}$

$\implies\tt{Area\:of\:triangle=939.1cm}$

Now,

• To find the longest altitude we have to take Shortest side as a base.

$\implies\sf{Area\:of\:triangle=\dfrac{1}{2}\times{Base}\times{Height}}$

$\implies\sf{939.1cm=\dfrac{35}{2}h}$

$\implies\sf{939.1\times{2}=35h}$

$\implies\sf{h=\dfrac{1878.2}{35}}$

$\implies\sf{h=53.66cm}$

Hence, the length of it's longest altitude us 53.66cm.