Question

quadrilateral klmn is similar to quadrilateral opqr. find the measure of side qr. figures are not drawn to scale.
two quadrilaterals: klmn with sides nm=4, ml=6; opqr with side qp=22.8

Explanation:

Step1: Identify corresponding sides

Since quadrilateral KLMN ~ OPQR, side ML (length 6) corresponds to side PQ (length 22.8), and side MN (length 4) corresponds to side QR (let's call its length \( x \)).

Step2: Set up proportion

The ratio of corresponding sides in similar figures is equal. So, \(\frac{ML}{PQ} = \frac{MN}{QR}\)

Substitute the known values: \(\frac{6}{22.8} = \frac{4}{x}\)

Step3: Solve for \( x \)

Cross - multiply: \(6x = 22.8\times4\)

Calculate \(22.8\times4 = 91.2\)

Then, \(x=\frac{91.2}{6}\)

\(x = 15.2\)

Answer:

The measure of side QR is \(15.2\)