In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)
Options:
(A) 20/7
(B) 28/5
(C) 9/2
(D) 35/4
Official Answer Key:
B
Step-by-Step Solution & Explanation
Area of parallelogram PQRS can be computed two ways using its two pairs of parallel sides as bases, with PT and PV as the corresponding heights (PT ⊥ QR, PV ⊥ RS). Area = QR × PT = RS × PV. Since PQRS is a parallelogram, QR = PS = 7 cm (opposite sides equal). So Area = 7 × 4 = 28 cm². Then RS = Area / PV = 28/5 cm. Answer: (B) 28/5. *Distractor note:* (A) 20/7 results from dividing 20 (wrong area) by 7; (D) 35/4 comes from swapping which side pairs with which height.
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