Question
One square has twice the area of another square. Explain why it is impossible for both squares to have side lengths that are whole numbers.
Answers
Reiny
The areas of two similar squares are proportional to the square of their corresponding sides
let the side of the smaller be x and the side of the larger be y
then x^2 : y^2= 1 : 2
2x^2 = y^2
y = (√2)(x)
suppose x is a whole number, then √2 times a whole number cannot be a whole number.
let the side of the smaller be x and the side of the larger be y
then x^2 : y^2= 1 : 2
2x^2 = y^2
y = (√2)(x)
suppose x is a whole number, then √2 times a whole number cannot be a whole number.