Question

In the following diagram line CF is parallel to line CD. Segment DE has a length that is 4 inches greater than the length of CD. If FG= 15 inches and FE=36 inches then determine the length of CD

Answer 1

Answer: CD = 10

Identify the given information. 
FG = 15
GE = 21
FE = 36
CD = x
DE = x + 4

Form your equation. Due to the Side-Splitter Theorem, FG/GE = CD/DE.
15/21 = x/x + 4

Cross-multiply and solve.
15(x + 4) = 21x            Distributive Property
15x + 60 = 21x           Subtract 15x from both sides
60 = 6x                      Divide by 6 to both sides
x = 10                         Answer!

Answer 2

The length of side CD is; 10

What is the side length of the triangle?

From the given triangles, we can see that;

FG = 15

GE = 21

FE = 36

CD = x

DE = x + 4

Using the side splitter theorem, we can form the equality as;

FG/GE = CD/DE.

Plugging in the relevant values gives;

15/21 = x/(x + 4)

Cross-multiply to get;

15(x + 4) = 21x            

Using the Distributive Property of equality gives;

15x + 60 = 21x          

Using subtraction property of equality to subtract 15x from both sides to get;

60 = 6x

Using the Distributive Property of equality, divide both sides by side by 6 to get;

x = 10

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