Problem 10 · 2024 Math Kangaroo
Medium
Number Theory
primessum-constraint
Ardal fences a rectangular plot of land using 40 m of fence. Every side length of the rectangle is a prime number. What is the largest possible area of the plot?
Show answer
Answer: B — 91 m²
Show hints
Hint 1 of 2
The two side lengths add to half the perimeter; both must be prime.
Still stuck? Show hint 2 →
Hint 2 of 2
For a fixed sum, the product (area) is largest when the two numbers are closest together.
Show solution
Approach: find the prime pair summing to 20 with largest product
- Perimeter 40 means the two sides add to 20, and both are prime.
- Prime pairs adding to 20: (3,17), (7,13); their products are 51 and 91.
- The largest area is 7 x 13 = 91 m^2.
Mark:
· log in to save