Answer:
[tex]D(x)= x\sqrt{2}[/tex]
Step-by-step explanation:
Given
[tex]Side = x[/tex]
Required
Represent the diagonal as a function
Using Pythagoras theorem, the diagonal is:
[tex]D^2= Side^2 + Side^2[/tex]
Substitute x for Side
[tex]D^2= x^2 + x^2[/tex]
[tex]D^2= 2x^2[/tex]
Take the square root of both sides
[tex]D= \sqrt{2x^2[/tex]
Split
[tex]D= \sqrt{2} * \sqrt{x^2[/tex]
[tex]D= \sqrt{2} * x[/tex]
[tex]D= x\sqrt{2}[/tex]
Express as a function.
[tex]D(x)= x\sqrt{2}[/tex]
