KVPY SA Exam 2015 Question Paper

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Question : 10 of 80

Marks: +1, -0

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

$x=y$
$x=2y$
$2x=y$
$x=3y$

Solution:

area (I)

= x.2y + 1/2 (2y + y) x.

=2xy+{3xy}/2={7xy}/2

area (II)

= 2x.2y- 1 /2√2 y. √2 y.

= 4xy - y^ 2

∴ area (I) = area (II)

{7xy}/2=4xy - y^ 2

⇒

7xy = 8xy - 2y^2

⇒

2y^2 = xy

⇒

[2y=x]

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