Question

If H is the midpoint of GE and J is the midpoint of FE, determine the following lengths.

Answer 1

Answer: The value of x is 5, the length of HJ is 8 and the length of 4.

Explanation:

It is given that H is the midpoint of GE and J is the midpoint of FE.

According to midpoint theorem the line segment connecting the midpoint of two sides is parallel to the three side and its length is half of the third side.

Since JH is connecting the midpoints.

$HJ=\frac{1}{2} (GF)$

$x+3=\frac{1}{2} (4x-4)$

$x+3=2x-2$

$x=5$

The value of x is 5.

$HJ=x+3=5+3=8$

$JE=x-1=5-1=4$

Therefore HJ=8 and JE=4.

Answer 2

HJ is a mid- segment,  GF=2HJ
so 
4x-4 =2(x+3)
4x-4=2x+6
2x=10
x=5
HJ= x+3=5+3=8
JE=x-1=5-1=4