Primary Divisonal 2012/6

Problem for Primary Group from Divisional Mathematical Olympiad will be solved here.
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Phlembac Adib Hasan
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Primary Divisonal 2012/6

Unread post by Phlembac Adib Hasan » Thu Dec 11, 2014 1:21 pm

In this diagram, the area of the larger square is three times of the smaller one. The area of the black shaded part is $12$ square unit. Find the area of the bigger square.
a.png (1.88 KiB) Viewed 3037 times
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Re: Primary Divisonal 2012/6

Unread post by tanmoy » Thu Dec 11, 2014 2:27 pm

Suppose,the area of the larger square is $x^{2}$ and the area of the smaller square is $y^{2}$.
$\frac{1}{2}\times (\sqrt{3}y+y)(\sqrt{3}y-y)=12$
Or,$\frac{1}{2}\times (3y^{2}-y^{2})=12$
$\therefore x^{2}=36$
$\therefore$ The area of the bigger square is $36$ square unit :)
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