Problem 11 · 2010 Math Kangaroo
Medium
Geometry & Measurement
areasquare-area
In the figure, ABCE is a square. CDE and BCF are equilateral triangles. The length of AB is 1. How long is FD?
Show answer
Answer: A — \(\sqrt{2}\)
Show hints
Hint 1 of 2
Place the unit square on coordinates and find where the two triangle tips D and F land.
Still stuck? Show hint 2 →
Hint 2 of 2
Then just measure the distance from D to F.
Show solution
Approach: coordinates for the two apex points
- Take the unit square A(0,0), B(1,0), C(1,1), E(0,1).
- The equilateral tips are D(1/2, 1+sqrt3/2) above EC and F(1-sqrt3/2, 1/2) left of BC.
- Then FD² = (sqrt3/2 - 1/2)² + (1/2 + sqrt3/2)² = 2, so FD = sqrt2.
Mark:
· log in to save