Discussion
If the height of triangle is decreased by 40% and its base is increased by 40%. What will be the area percentage change in its area?
Answer: C
The area shows a 16% decrease.
The area of a triangle is \(\frac{1}{2} \times \text{base} \times \text{height}\), so it changes by the product of the two factors:
\[ \begin{aligned} \text{new area} &= 1.40 \times 0.60 = 0.84 \\ \text{change} &= 0.84 - 1 = -0.16 \end{aligned} \]
That is a 16% decrease. A +40% and a −40% change do not cancel, because the 40% decrease is taken of a larger product. The shortcut \(a + b + \frac{ab}{100} = 40 - 40 - 16 = -16\) gives the same result, which rules out the 20% and 12% options.
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