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ABC & BDE are two equilateral …

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ABC & BDE are two equilateral triangle such that D is tbe midpoint of BC find the ratio of the area of triangle ABC & BDE

Posted by Tanveer Arhaan 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let the side of triangle = a
{tex}\therefore{/tex} BC = a {tex}\Rightarrow{/tex} BD = {tex}\frac{a}{2}{/tex}
Now area({tex}\triangle{/tex}BDE) = {tex}\frac{\sqrt{3}}{4}{/tex}({tex}\frac{a}{2}{/tex})² = {tex}\frac{\sqrt{3}}{4}{/tex}{tex}\frac{a^2}{4}{/tex} = {tex}\frac{1}{4}{/tex}({tex}\frac{\sqrt{3}}{4}{/tex}a²) = {tex}\frac{1}{4}{/tex}area ({tex}\triangle{/tex}ABC).
or area({tex}\triangle{/tex}BDE) = {tex}\frac{1}{4}{/tex}area ({tex}\triangle{/tex}ABC).
Hence proved.

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