zig-zag (Solution)

Not hard but I thought this was cute enough to include. Lots of ways to solve it, here’s probably the best way?

• Realize that the 45° trangle will have equal side lengths, so let’s call that \(x\).
• Then realize the the ratio of the side lengths of the big triangle will be 3 to 2

\[\begin{align*} \frac{3}{2} &= \frac{3+x}{x} \\ x &= 6 \end{align*}\]

The length of the black line is the same as the sum of the two sides of the big triangle, so \(6 + 9 = 15\).