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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