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 ?
Answer & explanation
Correct answer: option 1
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.