Question

The dimensions of a rectangular community garden are 47 ft by 27 ft. The gardeners plan to divide the garden into​ equal-sized square plots. What is the greatest possible side length of each square​ plot? Use pencil and paper. How many square plots will there be with this side​ length? What will be the total area of the square​ plots? Explain how you can use the total area to check your work.

Answer 1

the greatest possible length of each square plot is 1 ft.

1,269 square plots

Explanation:

Since the plots are going to be squares then the width and length need to be the same. This means that the largest size of these plots would be calculated as the largest common divisor of the length and width of the garden. In this scenario, since 47 only has two divisors 1 and 47, and 27 is not divisible by 47 then the GCD of these two numbers would be 1. Meaning that the greatest possible length of each square plot is 1 ft.

To calculate the total number of plots needed we divide the square footage of the garden by the square footage of each individual plot like so...

47 * 27 = 1,269 sq. ft.

1 * 1 = 1 sq. ft.

1,269 / 1 = 1,269 plots

Finally, we see that we need a total of 1,269 square plots to cover that same area of the garden.