🦘 Math Kangaroo Grade All Felix 1-2 Ecolier 3-4 Benjamin 5-6 Kadett 7-8 Junior 9-10 Student 11-12 ⇄ switch contest
2012 Math Kangaroo

Problem 3

Problem 3 · 2012 Math Kangaroo Easy
Number Theory factor-pairs

How many different rectangles with area 60 and whole-numbered side lengths are there?

Show answer
Answer: B — 6
Show hints
Hint 1 of 2
A rectangle is fixed by a pair of side lengths whose product is 60.
Still stuck? Show hint 2 →
Hint 2 of 2
Count the unordered factor pairs of 60.
Show solution
Approach: count factor pairs of 60
  1. A rectangle with whole sides and area 60 corresponds to a factor pair of 60.
  2. The pairs are 1×60, 2×30, 3×20, 4×15, 5×12 and 6×10.
  3. That is 6 different rectangles.
Mark: · log in to save