Question

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

• A. $x$ = 15, $y$ = 9
• B. $x$ = 9, $y$ = 15
• C. $x$ = 14, $y$ = 9
• D. $x$ = 15, $y$ = 10

Answer 1

The correct option is A

$x$ = 15, $y$ = 9

Given, $AB=AC$
$⟹94=6x+4⟹6x=90⟹x=15$


In $△ABD$ and $△ACD$,
(i) $\angle ADB=\angle ADC={90}^{\circ }$ ... (given)
(ii) AB = AC ... (given)
(iii) AD = AD ... (common side)
$\Rightarrow$$△ABD\cong △ACD$ ... (RHS congruence rule)

Then, $BD=CD$ ... (CPCT)
$\Rightarrow 2y–7=11\Rightarrow 2y=18\Rightarrow y=9$