Question

quadrilateral cdef is similar to quadrilateral ghij. find the measure of side gh. round your answer to the nearest tenth if necessary.
f
e
47
c 16 d
j
i
10
g h

Explanation:

Step1: Identify corresponding sides

Since quadrilateral CDEF ~ GHIJ, sides FC corresponds to JG, and CD corresponds to GH. So the ratio of FC to JG equals the ratio of CD to GH.
Let \( GH = x \). We know \( FC = 47 \), \( JG = 10 \), \( CD = 16 \). So the proportion is \( \frac{FC}{JG}=\frac{CD}{GH} \), i.e., \( \frac{47}{10}=\frac{16}{x} \).

Step2: Solve for x

Cross - multiply: \( 47x = 10\times16 \)
\( 47x = 160 \)
Then \( x=\frac{160}{47}\approx3.4 \) (rounded to the nearest tenth)

Answer:

\( 3.4 \)