Discussion
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.)
Answer: B
RS is 28/5 cm.
The area of a parallelogram is any side times the perpendicular distance to it from the opposite side. PT is the height on base QR, and PV is the height on base RS.
\[ \begin{aligned} QR \times PT &= RS \times PV \\ 7 \times 4 &= RS \times 5 \\ RS &= \frac{28}{5} = 5.6\ \text{cm} \end{aligned} \]
QR equals PS = 7 cm because opposite sides of a parallelogram are equal. 20/7 is PT times PV divided by PS, which mixes the two heights, and 35/4 is PS times PV over PT, which pairs each height with the wrong base.
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