Question : Given that the ratio of the altitude of two triangles is 4 : 5, the ratio of their areas is 3 : 2, the ratio of their corresponding bases is:
Option 1: 8 : 15
Option 2: 15 : 8
Option 3: 5 : 8
Option 4: 8 : 5
Correct Answer: 15 : 8
Solution :
The area of a triangle $=\frac{1}{2} \times \text{base} \times \text{height}$
Given that the ratio of the altitudes of two triangles is 4 : 5 and the ratio of their areas is 3 : 2.
$\frac{\text{Area of Triangle 1}}{\text{Area of Triangle 2}} = \frac{\text{Base of Triangle 1} \times \text{Height of Triangle 1}}{\text{Base of Triangle 2} \times \text{Height of Triangle 2}}$
$⇒\frac{3}{2} = \frac{\text{Base of Triangle 1} \times 4}{\text{Base of Triangle 2} \times 5}$
$⇒\frac{\text{Base of Triangle 1}}{\text{Base of Triangle 2}}=\frac{3\times 5}{2\times 4}=\frac{15}{8}$
Hence, the correct answer is 15 : 8
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