Given:
IJ = v + 30
HK = v
To find:
The value of HK
Solution:
By Triangle mid-segment theorem:
If a segment joining midpoints of two sides of a triangle, then the segment is parallel to the third side and is half of its length.
[tex]$\Rightarrow HK = \frac{1}{2}\times IJ[/tex]
[tex]$\Rightarrow v= \frac{1}{2}\times (v+30)[/tex]
Multiply by 2 on both sides.
[tex]$\Rightarrow 2\times v= 2\times\frac{1}{2}\times (v+30)[/tex]
[tex]$\Rightarrow 2 v= v+30[/tex]
Subtract v from both sides.
[tex]$\Rightarrow 2 v-v= v+30-v[/tex]
[tex]$\Rightarrow v=30[/tex]
Therefore HK is 30.
