CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.4 Question 8
8. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is
(A) 2:1 (B) 1:2 (C) 4:1 (D) 1:4
Solution
Given: ABC and BDE are two equilateral triangles and D is the mid-point of BC.
Any two equilateral triangles are similar because each angle is equal to 60 degrees.
Therefore,
~
(1)
{The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides}
But, we have BC = 2BD because D is the mid-point of BC. (2)
Putting (2) in (1), we get
Therefore, answer is (C)
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