Question

In the diagram below of triangle CDE,

F is the midpoint of CE and G is the
midpoint of DE.If FG 5x – 2, and
24 + 3x, what is the measure of
CD
CD?
E
=
Answer:
CD=
F
G
=
C
+
D

Answer 1

CD = 36

Explanation:

given a segment FG joining the midpoints of 2 sides of the triangle, then

segment FG is half the length of the third side , that is

FG =
`(1)/(2)` CD , so

5x - 2 =
`(1)/(2)` (24 + 3x ) ← multiply through by 2 to clear the fraction

10x - 4 = 24 + 3x ( subtract 3x from both sides )

7x - 4 = 24 ( add 4 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4

Then

CD = 24 + 3x = 24 + 3(4) = 24 + 12 = 36