Question : In a ΔPRQ, AB is drawn parallel to QR, cutting sides at A and B where the length of PQ = 6 cm, length of QR = 8 cm, and length of QA = 3 cm. What is the length of AB?
Option 1: 4 cm
Option 2: 4.2 cm
Option 3: 3.5 cm
Option 4: 2.4 cm
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Correct Answer: 4 cm
Solution :
PQ = 6 cm
QR = 8 cm
QA = 3 cm
Since AB $\parallel$ QR,
$\angle PAB$ = $\angle PQR$
$\angle PBA$ = $\angle PRQ$
So, $\triangle PAB$ ~ $\triangle PQR$
⇒ $\frac{PA}{PQ}$ = $\frac{AB}{QR}$
⇒ $\frac{3}{6}$ = $\frac{AB}{8}$
⇒ AB = $\frac{8}{2}$ = 4 cm
Hence, the correct answer is 4 cm.
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