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Home » ABC and BDE are two equilateral triangles such that D is the midpoint of BC. Ratio of these area of triangles ABC and BDE is (a) 2 : 1 (b) 1 : 4 (c) 1 : 2 (d) 4 : 1
ABC and BDE are two equilateral triangles such that D is the midpoint of BC. Ratio of these area of triangles ABC and BDE is (a) 2 : 1 (b) 1 : 4 (c) 1 : 2 (d) 4 : 1
CBSE | Class 10 | Exercise MCQ | Maths | RS Aggarwal | Triangles
ABC and BDE are two equilateral triangles such that D is the midpoint of BC. Ratio of these area of triangles ABC and BDE is (a) 2 : 1 (b) 1 : 4 (c) 1 : 2 (d) 4 : 1

Correct Answer: (d) 4 : 1

Explanation:

Given,

ABC and BDE are two equilateral triangles

D is the midpoint of BC and BDE is also an equilateral triangle.

E is also the midpoint of AB.

D and E are the midpoint of BC and AB.

In a triangle,

The line segment that joins midpoint of the two sides of a triangle is parallel to the third side and is half of it.

???????? ǁ ???????? ???????????? ???????? = ½ ????????

In ∆ABC and ∆EBD,

∠???????????? = ∠???????????? (???????????????????????????????????????????????????? ????????????????????????)

∠???? = ∠???? (????????????????????????)

By AA-similarity criterion,

∆ABC ~ ∆EBD

If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

\therefore \frac{{area(\Delta ABC)}}{{area(\Delta DBE)}} = {\left( {\frac{{AC}}{{ED}}} \right)^2} = > {\left( {\frac{{2ED}}{{ED}}} \right)^2} = > \frac{4}{1}

 

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