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Geometry

by ssgmatter » Sat Jun 12, 2010 10:26 am
An equilateral triangle ABC is inscribed in square ADEF, forming three right
triangles: ADB, ACF and BEC. What is the ratio of the area of triangle BEC to
that of triangle ADB?

Ans: 2
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by ayushiiitm » Sat Jun 12, 2010 4:35 pm
See in my diagram first that is attached (the best i could make with paint tools of MS)

Now we have to apply simple pythogoras and equilateral triangle property

Side AC=side AB

that gives

l^2+(l-x)^2=l^2+(l-y)^2

i.e on solving the terms cancel each other and we get x=y

On equating other sides BC=AB we find x=y=L/2

Now area of ADB=1/2*L*L/2

area of BEC= 1/2*L/2*L/2

ratio=2


I hope you understand when you put all these steps on paper, using the figure i have attached

Let me know, If it helped
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