Question

In $△ABC$ if $m\angle B={90}^{\circ }$ and $AB=BC$ then $AC:BC=$ ____.

• A. $\sqrt{2}:1$
• B. $1:2$
• C. $1:\sqrt{2}$
• D. $1:3$

Answer 1

The correct option is A $\sqrt{2}:1$

In $△ABC,m\angle B={90}^{\circ }$
$AB=BC=x$ say.
According to Pythagoras's theorem,
$A{C}^2=A{B}^2+B{C}^2$
$=x^2+x^2$
$=2x^2$
$\therefore AC=\sqrt{2}x$
Now, $AC:BC\sqrt{2}x:x$
$=\sqrt{2}:1$.