Question

Ratio of areas of two triangles with equal heights is 2 : 3. If base of the smaller triangle is 6 cm then what is the corresponding base of the bigger triangle ?

Answer 1

\[\frac{\text{ Area of smaller triangle }}{\text{ Area of bigger triangle }} = \frac{2}{3}\]
\[ \Rightarrow \frac{\frac{1}{2} \times \text{Height of smaller triangle } \times \text{ Base of smaller triangle }}{\frac{1}{2} \times \text{ Height of bigger triangle } \times \text{ Base of bigger triangle }} = \frac{2}{3}\]
\[ \Rightarrow \frac{6}{\text{ Base of bigger triangle }} = \frac{2}{3}\] 

\[\Rightarrow \text{ Base of bigger triangle } = \frac{3}{2} \times 6\]
\[ = 9\]