Question

What is the length of AC?

Answer 1

ABCD is a rectangle with length AB$=\sqrt{8}$cm and breadth AD$=\sqrt{2}$cm

Since opposite sides of rectangle are equal

$\Rightarrow AD=BC=\sqrt{2}$cm

Now each angle in a rectangle is at ${90}^o$

$\Rightarrow \angle DCB=\angle CBA=\angle BAD=\angle ADC={90}^o$

Now In $\Delta CAB$

AC is the hypotenuse, AB is the base and CB is the altitude by Pythagoras theorem.

$(AC{)}^2=(CB{)}^2+(AB{)}^2$

$(AC{)}^2=(\sqrt{2}{)}^2+(\sqrt{8}{)}^2$

$(AC{)}^2=2+8$

$(AC{)}^2=10$

$AC=\sqrt{10}$cm.