Using the information given in the figure, find the values of $x$ and $y$ .

$x$ = 15, $y$ = 10

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$x$ = 15, $y$ = 9

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$x$ = 14, $y$ = 9

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$x$ = 9, $y$ = 15

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Solution

The correct option is B
$x$ = 15, $y$ = 9

Given, $A B = A C$
$⟹ 94 = 6 x + 4 ⟹ 6 x = 90 ⟹ x = 15$

In $△ A B D$ and $△ A C D$ ,
(i) $∠ A D B = ∠ A D C = 90^{\circ}$ ... (given)
(ii) AB = AC ... (given)
(iii) AD = AD ... (common side)
$\Rightarrow$ $△ A B D ≅ △ A C D$ ... (RHS congruence rule)

Then, $B D = C D$ ... (CPCT)
$\Rightarrow 2 y - 7 = 11 \Rightarrow 2 y = 18 \Rightarrow y = 9$

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