Question

Triangle CDF is similar to triangle EGF

(ACDF ~ AEGF). What is the value of x?

A. 15

B.11

C. 9

D. 6

Answer 1

B.11

Explanation:

Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

From the image, CF corresponds to EF, CD corresponds to EG and DF corresponds to GF.

DF = DE + EF = 7 + 5 = 12

Since Triangle CDF is similar to triangle EGF. hence:

`(CF)/(EF) =(DF)/(GF) \\\\(CF)/(5)=(12)/(4) \\\\CF=(12*5)/(4)\\\\CF=15`

We can see that:

CF = CG + GF (line segment addition postulate)

CF = x + 4

15 = x + 4

x = 15 - 4

x = 11