Golden Thoughts

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

$2 \times3 \times4 \times5 + 1 = 11^2$
$21 \times22 \times23 \times24 + 1 = 505^2$
Show that if you add $1$ to the product of four consecutive numbers the answer is ALWAYS a perfect square.