Question

quadrilateral ijkl is similar to quadrilateral mnop. find the measure of side pm. figures are not drawn to scale.
l 5 k
3.7
i j
p 10 o
m n

Explanation:

Step1: Determine the scale factor

Since the quadrilaterals are similar, the ratio of corresponding sides is equal. The side \( LK = 5 \) in quadrilateral \( IJKL \) corresponds to side \( PO = 10 \) in quadrilateral \( MNOP \). The scale factor from \( IJKL \) to \( MNOP \) is \( \frac{10}{5}=2 \).

Step2: Find the length of \( PM \)

The side \( LI = 3.7 \) in quadrilateral \( IJKL \) corresponds to side \( PM \) in quadrilateral \( MNOP \). Using the scale factor, we multiply the length of \( LI \) by the scale factor. So, \( PM = 3.7\times2 = 7.4 \).

Answer:

\( 7.4 \)