MathNet 2021 — Part 08 Question 45

Question 45

A square of side length $2$ is divided into four triangles as shown. All three shaded triangles have equal areas. What is the area of the white triangle?

Question illustration

$\frac{1+\sqrt5}{2}$
$\frac85$
$2$
$3\sqrt5-5$
$6-2\sqrt5$