Question

quadrilateral cdef is similar to quadrilateral ghlj. find the measure of side gh.
round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify corresponding sides

Since quadrilaterals CDEF and GHLJ are similar, corresponding sides are proportional. Side ED (length 16) corresponds to side IH (length 59), and side CD (length 23) corresponds to side GH (let's call its length \( x \)).

Step2: Set up proportion

The proportion of corresponding sides is \( \frac{ED}{IH} = \frac{CD}{GH} \). Substituting the known values: \( \frac{16}{59} = \frac{23}{x} \).

Step3: Solve for \( x \)

Cross - multiply to get \( 16x = 59\times23 \). First, calculate \( 59\times23 = 1357 \). Then, \( x=\frac{1357}{16} \).

Step4: Calculate the value

\( \frac{1357}{16}=84.8125 \), which rounds to 84.8 when rounded to the nearest tenth.

Answer:

84.8