KVPY SA Exam 2012 Question Paper

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Question : 63 of 80

Marks: +1, -0

In a triangle ABC, it is known that AB = AC. Suppose D is the mid-point of AC and BD = BC = 2. Then the area of the triangle ABC is

2
$2√2$
$√7$
$2√7$

Solution:

We know

\AB^2 + \BC^2 = 2 (\CD^2 + \BD^2)

AB^2+4=2(\AB^2/4+4)

\AB^2+4=\AB^2/2+8

\AB^2/2=4⇒\AB^2=8

\AB=2√2

Now Area

=1/2×2×√7

=√7

square unit.

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