Question

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

Explanation:

Step1: Identify Corresponding Sides

Since quadrilaterals \( CDEF \) and \( GHIJ \) are similar, their corresponding sides are proportional. Side \( ED \) in \( CDEF \) corresponds to side \( IH \) in \( GHIJ \), and side \( CD \) in \( CDEF \) corresponds to side \( GH \) in \( GHIJ \). So, \( \frac{ED}{IH}=\frac{CD}{GH} \).

Step2: Substitute Known Values

We know \( ED = 16 \), \( IH = 59 \), and \( CD = 23 \). Substitute these into the proportion: \( \frac{16}{59}=\frac{23}{GH} \).

Step3: Solve for \( GH \)

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

Step4: Calculate the Value

\( \frac{1357}{16}=84.8125 \approx 84.8 \) (rounded to the nearest tenth).

Answer:

\( 84.8 \)