Question

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

Explanation:

Step1: Identify corresponding sides

Since quadrilateral \( IJKL \) is similar to quadrilateral \( MNOP \), the corresponding sides are proportional. Side \( LK \) (length 5) corresponds to side \( PO \) (length 10), and side \( LI \) (length 3.7) corresponds to side \( PM \) (let's call its length \( x \)).

Step2: Set up proportion

The ratio of corresponding sides should be equal. So, \(\frac{LK}{PO}=\frac{LI}{PM}\). Substituting the known values, we get \(\frac{5}{10}=\frac{3.7}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \( 5x = 10\times3.7 \). Then, \( 5x=37 \). Divide both sides by 5: \( x=\frac{37}{5}=7.4 \).

Answer:

The measure of side \( PM \) is \( 7.4 \).