Question

the quadrilaterals abcd and jklm are similar. find the length x of \overline{jk}.

Explanation:

Step1: Determine the scale factor

Since the quadrilaterals are similar, the ratio of corresponding sides is equal. Let's take the sides \( AD = 2 \) and \( JM = 1.6 \). The scale factor \( k \) is \( \frac{JM}{AD}=\frac{1.6}{2} = 0.8 \).

Step2: Find the length of \( JK \)

The corresponding side of \( JK \) in quadrilateral \( ABCD \) is \( AB = 4 \). So, we multiply \( AB \) by the scale factor to get \( JK \).
\( x=AB\times k = 4\times0.8 = 3.2 \)

Answer:

\( 3.2 \)