Question

A farmer has a rectangular piece of land measuring 840 meters by 396 meters. He divides it into equal square plots of equal size. What is the maximum area of one square plot?.......PLLLZZZ HELP

Answer 1

The maximum area of one square plot is 144
`m^2`

Explanation:

Start by looking at what are the greater common factor of both provided dimensions (840 and 396) to find what the numbers are they both can be divided by evenly:

`840=2^3\,*\,3\,*\.5\,*\,7\\396=2^2\,*\,3^2\,*\,11`

therefore, both numbers can be divided by
`2^2\,*\,3=12`

Which then gives:

`(840)/(12) =70\\(396)/(12) =33`

Then, one can divide the longest side (840 m) into 70 sections of 12 meters each, and the shortest side of the piece of land (396 m) into 33 sections of 12 meters each.

Then we can have a total of 33 * 70 = 2310 smaller lots of 12 m by 12 m

That is smaller plots of a total area 144 square meters