Question

In the image to the right, DB∥EF. Find the value of x and then find the length of DF. Set up a proportion and solve for the measure. Show your work and label your answer to get full points.

Answer 1

Answer: x=5, DF=12

Explanation:

By the triangle proportionality theorem,

(x+7)/16 = 3/4

(x+7)/16 = 12/16

So x+7=12 -> x=5

Meaning DF=5+7=12

Answer 2

12

Explanation:

Two triangles are similar so we can find the length of DF using the sides' proportion:

BC/EC = DC/FC

7/4 = (x+7+16)/16 cross multiply expressions:

112 = 4x + 92 subtract 92 from both sides

20 = 4x divide both sides by

5 = x

since DF is x+7 then its length is 12