Answer:
The diagonal is irrational because it is a product of a rational and an irrational number
Step-by-step explanation:
The options are not given. However, the question is still answerable.
Given
Shape: Square
Length: Rational
Since the side length is said to be rational, I'll answer the question based on whether the diagonal is rational or not.
Having said that:
The diagonal (d) of a square with side length (l) is calculated using Pythagoras theorem.
[tex]d^2 = l^2 + l^2[/tex]
[tex]d^2 = 2l^2[/tex]
Take positive square root of both sides
[tex]d = \sqrt{2l^2}[/tex]
Split:
[tex]d = \sqrt{2} * \sqrt{l^2}[/tex]
[tex]d = \sqrt{2} *l[/tex]
Recall that the side length (l) is rational.
However, [tex]\sqrt 2[/tex] is irrational.
So, the product of l and [tex]\sqrt 2[/tex] will be irrational
Hence:
The diagonal is irrational
