Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:
Option 1: Isosceles triangle
Option 2: Right-angled triangle
Option 3: Equilateral triangle
Option 4: Right isosceles triangle
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Correct Answer: Right isosceles triangle
Solution :
AB = $k$
BC = $k$
AC = $\sqrt2k$
⇒ AB
2
= $k^2$
⇒ BC
2
= $k^2$
⇒ AC
2
= $2k^2$
$\therefore$ AB
2
+ BC
2
= AC
2
and AB = BC
By Pythagoras theorem, $\triangle$ ABC is a right isosceles triangle.
Hence, the correct answer is 'Right isosceles triangle'.
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