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# geometry question

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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.

Dec 31, 2021

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The side length of the square is $\frac{21 + \sqrt{43}}{2}$, so $b = 43$.

Dec 31, 2021
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can you please include an explanation? i am mainly interested in how to solve it.

Guest Dec 31, 2021