In the figure given below, if the areas of the two regions are equal, then which of the following is true?

x = y

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x = 2 y

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2 x = y

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x = 3 y

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Solution

The correct option is B $x = 2 y$

Area of the first region,
$A_{1} = ar (O A D E) + ar (A B C D)$
$= 2 x y + \frac{1}{2} x (2 y + y)$

Area of the second region,
$A_{2} = ar (P Q R S) + ar (S T U V)$
$= 2 x y + (2 x - y) y$

Since $A_{1} = A_{2},$
$\frac{1}{2} x (2 y + y) = (2 x - y) y$
$\Rightarrow x = 2 y$

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