Question

quadrilateral hijk is similar to quadrilateral lmno. find the measure of side lm. figures are not drawn to scale.

Explanation:

Step1: Identify corresponding sides

Since quadrilateral \( HIJK \) is similar to quadrilateral \( LMNO \), the corresponding sides are proportional. Let's assume \( HK \) corresponds to \( LO \), and \( HI \) corresponds to \( LM \). From the diagram, \( HK = 6 \), \( LO = 48 \), and \( HI = 6.5 \). Let \( LM = x \).

Step2: Set up the proportion

The ratio of corresponding sides should be equal. So, \(\frac{HK}{LO}=\frac{HI}{LM}\). Substituting the known values, we get \(\frac{6}{48}=\frac{6.5}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \( 6x = 48\times6.5 \). First, calculate \( 48\times6.5 = 312 \). Then, \( x=\frac{312}{6}=52 \).

Answer:

The measure of side \( LM \) is \( 52 \).