Using the information given in the figure, find the values of $x$ and $y$ . (2 marks)

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Solution

Given, $A B = A C$
$⟹ 94 = 6 x + 4 ⟹ 6 x = 90 ⟹ x = 15 u n i t s$

(1 mark)
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)
$\Rightarrow 2 y - 7 = 11 \Rightarrow 2 y = 18 \Rightarrow y = 9 u n i t s$ (1 mark)

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