Question

quadrilateral nopq is similar to quadrilateral rstu. find the measure of side ur. figures are not drawn to scale.
q 10 p
5
n o
u 4.8 t
r s

Explanation:

Step1: Identify corresponding sides

Since quadrilaterals NOPQ and RSTU are similar, their corresponding sides are proportional. In rectangle NOPQ, side QP = 10 and QN = 5. In rectangle RSTU, side TU = 4.8, and we need to find UR. Corresponding sides: QP corresponds to TU, and QN corresponds to UR.

Step2: Set up proportion

Let \( x \) be the length of UR. The proportion is \( \frac{QN}{UR} = \frac{QP}{TU} \), so \( \frac{5}{x} = \frac{10}{4.8} \).

Step3: Solve for \( x \)

Cross - multiply: \( 10x = 5\times4.8 \). Then \( 10x = 24 \), and \( x=\frac{24}{10}=2.4 \).

Answer:

The measure of side UR is \( 2.4 \).