ABCD is a square. Points P, Q are chosen on sides BC,CD such that BP=4, DQ=5 and ∠PAQ=45∘. The side length of ABCD can be written as\(\frac{a+\sqrt{b}}{2}\) where a,b are positive integers. Find b.
The side length of the square is $\frac{21 + \sqrt{43}}{2}$, so $b = 43$.
can you please include an explanation? i am mainly interested in how to solve it.
