/sci/ - Science & Math

Alright math wizards, I've got a problem and I CANNOT FUCKING SOLVE IT. If you think you're up for the challenge, and manage to prove the answer, you're a god in my books.

A Rectangle PQRS is placed inside a scalene triangle ABC. If the area of the triangle is constant, prove that the maximum area of the rectangle is one-half the area of the triangle.

To help you visualise it, vertice P of the rectangle would touch AB, vertice Q would touch AC, and vertices R and S both touch BC. Good luck.