IKMC 2027 - Grades 11-12 - Self-study SET 1 - Thematic Batch 3 Question 20

Question 20

Two straight rods lean against a rectangular doorway as shown. Their supporting endpoints are at heights u and v above the floor. What is the height of the rods’ intersection above the floor?

Question illustration

$\frac{uv}{u+v}$
$\frac{2uv}{(\sqrt{u}+\sqrt{v})^2}$
$\frac{\sqrt{uv}}{2}$
$\frac{u+v}{4}$
$\sqrt{\frac{u^2+v^2}{8}}$