Question

In the diagram below of triangle CDE,

F is the midpoint of CE and G is the
midpoint of DE.If FG = 35 - 3x,
and CD = 2x + 14, what is the
measure of FG?
Answer:
FG =
F
D
G
E

Answer 1

`\huge\boxed{\sf FG = 14}`

Explanation:

Statement:

Line segment joining the mid-points of two sides of the triangle is parallel and half of the third side.

According to the statement:

CD = 2(FG)

2x + 14 = 2(35 - 3x)

Distribute

2x + 14 = 70 - 6x

Add 6x to both sides

2x + 6x + 14 = 70

8x + 14 = 70

Subtract 14 to both sides

8x = 70 - 14

8x = 56

Divide 8 to both sides

x = 56/8

x = 7

So,

FG = 35 - 3x

FG = 35 - 3(7)

FG = 35 - 21

FG = 14

`\rule[225]{225}{2}`