Question : The area of the two triangles is in the ratio 5 : 3 and their heights are in the ratio 5 : 7. Find the ratio of their bases.
Option 1: 3 : 5
Option 2: 7 : 3
Option 3: 7 : 5
Option 4: 2 : 3
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Correct Answer: 7 : 3
Solution :
Area of triangle = $\frac{1}{2}×{\text{Base × Height}}$
$\frac{\text{Area of triangle 1}}{\text{Area of triangle 2}}=\frac{\frac{1}{2}\times \text{Base}_1 \times \text{Height}_1}{\frac{1}{2}\times \text{Base}_2 \times \text{Height}_2}$
⇒ $\frac{5}{3}=\frac{\text{Base}_1 \times 5}{\text{Base}_2 \times 7}$
⇒ $\frac{\text{Base}_1}{\text{Base}_2}=\frac{7}{3}$
Hence, the correct answer is 7 : 3.
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