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

(In reply to 3 Solutions to an impossible task by Jer)

This is implies PQ=√(85±42√2)
But 85±42√2 is irrational and so it cannot be written as X/Y.
The given task is impossible.

A very small point: PR=QR=√(85+42√2). PQ= sqrt(170+84sqrt(2)), close to sqrt(47651/165), that is 16.9939 and change.

Posted by broll on 2016-07-04 02:37:29