We made a computer to draw and print out all those rectangle

We made a computer to draw and print out all those rectangles whose sides measured in centimeters are whole numbers, and whose areas are not more than 100 square centimeters. (The nxk and the kxn rectangles are considered to be the same, therefore, they are printed out once!) Inside the rectangles we wrote their areas. How many such positive whole numbers are there between 1 and 100 that appear exactly twice on the rectangles? (Please write down your answer as clear as possible.)

Solution

k and n are thse sides of recatnagle

k*n < = 100

k < = 100/n

So, 100/n --- integer

n =1 , 2, 4, 5, 10, 20, 25, 50, 100 between 1 and 100

k = 100, 50, 25, 20, 10, 5, 4, 2, 1

So, set of such whole numbers which appear twice are 100, 50, 25, 20, 10, 5, 4, 2, 1