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A rectangle having integer length and width has a perimeter of 100 units. What is the number of square units in the least possible area?

 Jan 22, 2015

Best Answer 

 #1
avatar+130536 
+5

If the sides of the perimeter are integers, 1 is the minimum side length of any particular side. So, 49 would have to be the length of the adjacent side.....

Note  1 + 49  + 1 + 49 = 100 = the perimeter

So... the minimum square area would be (1) (49) = 49 square units...

Here's a graph of the situation with some of the integer possibilities......https://www.desmos.com/calculator/ap3s1jlsnv

Notice that after x = 1, the values of x from 2 to 25 inclusive all produce greater areas....!!!

 

 Jan 22, 2015
 #1
avatar+130536 
+5
Best Answer

If the sides of the perimeter are integers, 1 is the minimum side length of any particular side. So, 49 would have to be the length of the adjacent side.....

Note  1 + 49  + 1 + 49 = 100 = the perimeter

So... the minimum square area would be (1) (49) = 49 square units...

Here's a graph of the situation with some of the integer possibilities......https://www.desmos.com/calculator/ap3s1jlsnv

Notice that after x = 1, the values of x from 2 to 25 inclusive all produce greater areas....!!!

 

CPhill Jan 22, 2015

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