Question

the quadrilaterals abcd and jklm are similar. find the length x of \\(\overline{lm}\\). (images of two quadrilaterals: left has sides ab=2, bc=4, ad=4, cd=7; right has sides jk=2.8, kl=5.6, jm=5.6, lm=x) \\(x = \square\\)

Explanation:

Step1: Find the scale factor

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

Step2: Apply the scale factor to \( CD \)

The length of \( CD = 7 \). To find \( LM \) (corresponding to \( CD \)), we multiply \( CD \) by the scale factor. So \( LM=CD\times k = 7\times1.4 \).
\( 7\times1.4 = 9.8 \)

Answer:

\( 9.8 \)