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Maharashtra State BoardSSC (English Medium) 10th Standard

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 ?

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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 ?

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Solution

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

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

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Chapter 1: Similarity - Problem Set 1 [Page 27]

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