3. The base of a triangle is increased by $20 \%$ and its height is decreased by $15 \%$. What happens to its area?
A It decreases by $3 \%$
B It remains the same
C It decreases by $2 \%$
D It increases by $2 \%$
E It increases by $5 \%$
Solution
D

Suppose the original triangle has base $b$ and height $h$. The area of this triangle is $X$, where $X=\frac{1}{2}(b \times h)$.
When the base of the triangle is increased by $20 \%$, its base becomes $b^{\prime}=\frac{6}{5} b$. When its height is decreased by $15 \%$, its height becomes $h^{\prime}=\frac{17}{20} h$.
Therefore the area of the changed triangle is $X^{\prime}$, where $X^{\prime}=\frac{1}{2}\left(b^{\prime} \times h^{\prime}\right)=\frac{1}{2}\left(\frac{6}{5} b \times \frac{17}{20} h\right)=$ $\left(\frac{6}{5} \times \frac{17}{20}\right)\left(\frac{1}{2}(b \times h)\right)=\frac{102}{100} X$.
Therefore the effect of the changes is to increase the area of the triangle by $2 \%$.