Let ABCD be a square of a side length l, Let P, Q, R, S be points in the interiors of the sides AD, BC, AB, CD, respectively, such that PQ and RS intersect at right angles. If PQ = 3√34, then RS equals
3√34
PQ⊥RS
⇒c−a=b−d………(1)
⇒PQ=3√34
⇒PQ2=2716
⇒1+(a−c)2=2716………(2)
⇒RS=√(b−d)2+1………(3)
By equation (1), (2) and (3)
RS=3√34