Question : $\triangle \mathrm{ABC}$ is an isosceles triangle with $\angle \mathrm{ABC}=90^{\circ}$ and $\mathrm{AB}=\mathrm{BC}$. If $\mathrm{AC}=12 \mathrm{~cm}$, then the length of $\mathrm{BC}$ (in $\mathrm{cm}$) is equal to:
Option 1: $6 \sqrt{2}$
Option 2: $8$
Option 3: $6$
Option 4: $8 \sqrt{2}$
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Correct Answer: $6 \sqrt{2}$
Solution :
Given, $\triangle \mathrm{ABC}$ is an isosceles triangle with $\angle \mathrm{ABC}=90^{\circ}$, $\mathrm{AB}=\mathrm{BC}$, and $\mathrm{AC}=12 \mathrm{~cm}$
According to Pythagoras theorem,
$AC^2=AB^2+BC^2$
⇒ $12^2=2\times BC^2$
⇒ $BC^2= 72$
⇒ $BC=6\sqrt2$ cm
Hence, the correct answer is $6\sqrt2$.
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