In a $\triangle$ PRQ, AB is drawn parallel to QR, cutting sides at A and B where length of PQ = 6 cm, length of QR = 8 cm and length of QA = 3 cm. What is the length of AB ?

4.0 cm

Concept Used

In \(\Delta \)PAB = \(\Delta \)PQR

\(\angle\)PAB = \(\angle\)PQR (corresponding angles)

and \(\angle\)P is common.

Therefore, \(\Delta \)PAB is similar to \(\Delta \)PQR  (AA similarity criterion)

Since corresponding sides are proportional,

\(\frac{AB}{QR}\) = \(\frac{PA}{PQ}\)

AB = \(\frac{QR \;×\; PA}{PQ}\)

Calculation

AB = \(\frac{8 \;×\; 3}{6}\)

AB = 4 cm

Therefore, AB is 4 cm.