Question

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

Explanation:

Step1: Find the scale factor

Since the quadrilaterals are similar, the ratio of corresponding sides is equal. Let's take sides \( CD \) and \( ML \). The length of \( CD = 2 \) and \( ML = 2.8 \). The scale factor \( k \) is \( \frac{ML}{CD}=\frac{2.8}{2} = 1.4 \).

Step2: Calculate \( x \) (length of \( JK \))

The corresponding side of \( JK \) in quadrilateral \( ABCD \) is \( AB = 5 \). So, \( x = AB\times k \). Substituting the values, we get \( x = 5\times1.4 \).
\( x = 7 \)

Answer:

\( x = 7 \)