Question

ABC and BDE are two equilateral triangle such that BD = 2 / 3 BC find the ratio of areas of triangles ABC and BDE

Answer 1

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Answer 2

The ratio of areas of triangles ABC and BDE is 9:4.

Given:

ABC and BDE are two equilateral triangles such that BD=2/ 3BC.

To Find:

The ratio of areas of triangles ABC and BDE.

Solution:

ABC is an equilateral triangle.

⇒ AB = BC =AC

Also, BDE is an equilateral triangle.

⇒ BD = DE = BE

Area of an equilateral triangle = $\frac{\sqrt{3} }{4} *Side^{2}$

Area of triangle ABC = $\frac{\sqrt{3} }{4} *BC^{2}$

Area of triangle BDE = $\frac{\sqrt{3} }{4} *BD^{2}$

The ratio of triangles ABC and BDE

$=\frac{BC^{2} }{BD^{2} } \\ \\=\frac{9BC^{2} }{4BC^{2} } \\\\=\frac{9}{4}$

∴The ratio of areas of triangles ABC and BDE is 9:4.

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