2016 · Q61
A square is inscribed in a right-angled triangle with legs p and q, and has a common right angle with the triangle. The diagonal of the square is given by
Elementary MathematicsMensuration
- Apq/(p+2q)
- Bpq/(2p+q)
- C(√(2)pq)/(p+q)
- D2pq/(p+q)
Explanation
If the square has side s, similar triangles give s/p + s/q = 1. Hence s = pq/(p+q). Its diagonal is s√2 = √2·pq/(p+q), option C.