Question

In quadrilateral $PQRS$ above, what is the value of $a^2+b^2$ ?

• A. $8$
• B. $10$
• C. $11$
• D. $12$
• E. $13$

Answer 1

Answer: (E)

$13$

In the figure given above, the triangle $QRS$ is right angled triangle with hypotenuses at $QS$.

So by pythagoras theorem we get ${QS}^2=2^2+3^2$.

Similarly triangle $PQS$ is also right angles triangle with hypotenuses at $QS$.

So by pythagoras theorem we get ${QS}^2=2^2+3^2=a^2+b^2=13$,