Question

In the given figure, we have $ABCD$ is square. $PC=9$ cm, $PS=3$ cm, $AS=12$ cm. Find $AB$.

Answer 1

Using Pythagoras theorem, we can say that,

$a^2+b^2=c^2$

Since, the given diagram is a square, sides are equal

$\therefore a=b$

$\Rightarrow 2a^2=c^2$

Since given $c=12+9\Rightarrow c=21$

$\Rightarrow 2a^2={21}^2$

$\Rightarrow a=\frac{21}{\sqrt{2}}$

$\therefore AB=\frac{21}{\sqrt{2}}$