Question

quadrilateral lmno is similar to quadrilateral pqrs. find the measure of side pq. figures are not drawn to scale.
30
45
5.4

Explanation:

Step1: Identify corresponding sides

Corresponding sides: $OL = 30$, $SP = 5.4$, $LM = 45$, $PQ = x$ (unknown)

Step2: Set up similarity proportion

Since similar figures have proportional sides:
$\frac{PQ}{LM} = \frac{SP}{OL}$

Step3: Substitute known values

$\frac{x}{45} = \frac{5.4}{30}$

Step4: Solve for $x$

Multiply both sides by 45:
$x = 45 \times \frac{5.4}{30}$
$x = 1.5 \times 5.4$
$x = 8.1$

Answer:

$8.1$