An isosceles triangle PQR is such that ∠PRQ = 90^o. Point U is inside triangle PQR, such that UP =11, UQ=7 and UR=6.

Each of the legs PR and QR has length √(X/Y) where each of X and Y is a positive integer.

Find X and Y

Thank you, Armando and Jer, for your very clear explanations, in particular explaining why there is such a problem with 42*2^(1/2).

Interestingly, working from the opposite direction, WolframAlpha doesn't usually offer large multiples of square roots as a possible closed form, but 42*2^(1/2) comes up at once as a possibility for 59.3969696.

So I guess it is a 'known issue' in those circles, at least.

Posted by broll on 2016-06-11 20:50:40