Around the flowerbed

Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses found in every corner of the flowerbed and consumed them as little as possible.

a) At what distance are planted roses?
b) How many roses do you need?

Result

a =  1.75 m
n =  10

Solution:

$a = 525 = 3 \cdot 5^2 \cdot 7 \ \\ 350 = 2 \cdot 5^2 \cdot 7 \ \\ \text{GCD}(525, 350) = 5^2 \cdot 7 = 175 \ cm = 1.75 \ \text{m} \ \\$

$n = \dfrac{2(5.25+3.5)}{ a } = 10$

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