Question

Need help with this important work please

Answer 1

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.

$\Rightarrow HK = \frac{1}{2}\times IJ$

$\Rightarrow v= \frac{1}{2}\times (v+30)$

Multiply by 2 on both sides.

$\Rightarrow 2\times v= 2\times\frac{1}{2}\times (v+30)$

$\Rightarrow 2 v= v+30$

Subtract v from both sides.

$\Rightarrow 2 v-v= v+30-v$

$\Rightarrow v=30$

Therefore HK is 30.