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, and it is the same whichever pair of sides you use. PT is the height onto base QR, and QR = PS = 7 cm. PV is the height onto side RS.
\[ \begin{aligned} \text{Area} &= QR \times PT = 7 \times 4 = 28 \\ \text{Area} &= RS \times PV = 5\,RS \\ RS &= \frac{28}{5}\ \text{cm} \end{aligned} \]
The distractor 20/7 comes from 4 × 5 / 7, mixing the two heights; 35/4 comes from 7 × 5 / 4, putting the heights the wrong way round; 9/2 is simply (4 + 5)/2.
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