Discussion
The area of a quadrilateral is 227.2 cm2 and the length of the perpendiculars from the opposite vertices to a diagonal are 7.2 cm and 8.8 cm. What is the length of the diagonal ?
Answer: B
The diagonal is 28.4 cm.
A diagonal divides the quadrilateral into two triangles with the diagonal as their common base and the two perpendiculars as their heights:
\[ \begin{aligned} \text{Area} &= \tfrac{1}{2} d (h_{1} + h_{2}) \\ 227.2 &= \tfrac{1}{2} d (7.2 + 8.8) = 8d \\ d &= 28.4\ \text{cm} \end{aligned} \]
Forgetting the factor one half gives 14.2 cm, not an option; the other values do not satisfy the area formula (for example 8 × 26.8 = 214.4).
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