Question

quadrilateral defg is similar to quadrilateral hijk. find the measure of side ij. round your answer to the nearest tenth if necessary. figures are not drawn to scale. g f 14 d e 5 j i 47 h k

Explanation:

Step1: Identify corresponding sides

Since quadrilateral DEFG is similar to quadrilateral HIJK, the ratio of corresponding sides is equal. Let's assume side FG (length 14) corresponds to side JK (length 47), and side FE (length 5) corresponds to side IJ (let's call its length \( x \)).

Step2: Set up proportion

The proportion for similar figures is \(\frac{FG}{JK} = \frac{FE}{IJ}\). Substituting the known values: \(\frac{14}{47} = \frac{5}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \( 14x = 47\times5 \).
Calculate \( 47\times5 = 235 \). So, \( 14x = 235 \).
Then, \( x=\frac{235}{14}\approx16.8 \).

Answer:

\( 16.8 \)