Question

5.In ∆ABC, if r1=12, r2= 18,r3 = 36 then the length of the altitude through A isa) 32b) 26c) 18d) 24​

Answer 1

∴ The length of the altitude through $A$ is $18$

Step-by-step explanation:

Given;

For a $\bigtriangleup ABC$, $r_{1} =12$  , $r_{2} =18$ and $r_{3}=36$

The medians of a triangle intersect at a point called centroid that is two third of the distance from each vertex to the to the mid point of the opposite side.

By this theorem;

$\frac{AO}{AD}= \frac{2}{3}$

From figure,

$AO=12$

So,

⇒$AD=\frac{3}{2}AO$

⇒$AD=\frac{3}{2}\times 12$

∴$AD=18$

So the length of the altitude through $A$ is $18$