In the following figure, both the triangles are congruent where, $A C = 2 x - y, A B = 2 x + y$ , $R P = 2 u n i t s, P Q = 6 u n i t s$ .
What is the value of x and y?

x = 2, y = 1

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x = 1, y = 2

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x = 1, y = 1

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x = 2, y = 2

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Solution

The correct option is D $x = 2, y = 2$
In $△ A B C$ and $△ P Q R$ ,

$A B = P Q ∠ B A C = ∠ Q P R A C = P R$

Therefore, $△ A B C ≅ △ P Q R$ by SAS criteria.

$\Rightarrow A C = 2 x - y = 2 . . . . . . (i)$
$\Rightarrow A B = 2 x + y = 6.......... (i i)$
Adding (i) and (ii) we get,
$4 x = 8$
$\Rightarrow x = 2$
Substituting $x$ in (i), we get,
$\Rightarrow 2 \times 2 - y = 2$
$\Rightarrow y = 2$
$∴ x = 2 and y = 2$

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