Jenny drew the rectangle ABCD below that has one side of length 10 and the other 10√3.
She then drew in the line PQ to make a rectangle with C and B.
If the ratios AB : BC and BC : QC are equal, what is the length of BQ?
Solution
We know that AB : BC = BC : QC
BC = AB/√3, so QC = BC/√3 = 10/√3
By Pythagoras’ Theorem, BQ2 = BC2 + QC2
BQ2 = 102 + (10/√3)2
BQ2 = 102 + 102/3
BQ2 = 102 × 4/3
BQ2 = 400/3
So BQ = 20/√3.