Problem 15 · 2021 Math Kangaroo
Hard
Geometry & Measurement
perimeter
A large triangle is divided into smaller triangles as shown. The number inside each small triangle indicates its perimeter. What is the perimeter of the large triangle?
Show answer
Answer: C — 34
Show hints
Hint 1 of 2
Add up all the small perimeters; every inner edge gets counted twice.
Still stuck? Show hint 2 →
Hint 2 of 2
Subtract twice the total length of the shared interior edges to leave only the outer boundary.
Show solution
Approach: relate the sum of small perimeters to the outer boundary
- Adding every small triangle's perimeter counts each interior (shared) edge twice and each outer edge once: the labels total 10+9+15+13+11+12+20 = 90.
- So the large triangle's perimeter = 90 − 2×(total length of the interior edges).
- The interior edges in the figure add up to 28, leaving an outer perimeter of 90 − 56 = 34.
Mark:
· log in to save