Question

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

Explanation:

Step1: Identify corresponding sides

Since quadrilateral LMNO is similar to quadrilateral PQRS, the ratio of corresponding sides is equal. Let's assume side ON (length 3) corresponds to side SR (length 7.5), and side OL (length 4) corresponds to side SP (let's call its length \( x \)).

Step2: Set up the proportion

The ratio of similarity is the same for all corresponding sides. So, \(\frac{ON}{SR}=\frac{OL}{SP}\). Substituting the known values, we get \(\frac{3}{7.5}=\frac{4}{x}\).

Step3: Solve for \( x \)

Cross - multiply: \( 3x = 4\times7.5 \).
Calculate the right - hand side: \( 4\times7.5 = 30 \).
Then, \( x=\frac{30}{3}=10 \).

Answer:

The length of side SP is 10.