Problem 16 · 2022 Math Kangaroo
Hard
Geometry & Measurement
ratiogrid
The rectangle ABCD is made up of 12 congruent rectangles (see diagram). How big is the ratio \(\dfrac{AD}{DC}\)?
Show answer
Answer: A — \(\tfrac{8}{9}\)
Show hints
Hint 1 of 2
Let each small rectangle be w by h and read off how many stack along AD and along DC.
Still stuck? Show hint 2 →
Hint 2 of 2
Two equations relating w and h come from the two ways the small rectangles tile the big one.
Show solution
Approach: set up the small-rectangle dimensions from the tiling
- Give each of the 12 congruent rectangles width w and height h, and count how many line up along each side of ABCD.
- The horizontal and vertical fits give two relations between w and h, which fix the side lengths AD and DC.
- Their ratio AD/DC works out to 8/9.
Mark:
· log in to save