00:02
In this problem, we're asked to express the side length of a square as a function of the length d of the square's diagonal, and then to do the same thing with the area.
00:11
So let's begin by drawing a picture of our square.
00:16
So this square has all the sides are the same, so let's call that side length s.
00:24
And we have the diagonal of the square, which is length d.
00:32
So the goal is to find a function, find a function, where we plug in d and we get out s.
00:51
So if i told you that the diagonal was length 2, what would the length of the side be? that's the kind of formula we're looking for.
00:59
So to do this, we want to try and find some relationship between d and s.
01:04
And the easiest way to do this is to notice that we have this nice right triangle here.
01:10
So we can use the pythagorean theorem to get the relationship s squared plus s -square.
01:20
Equals d squared, which we can rewrite as two times s squared equals d squared.
01:30
Or if we want to get s as a function of d, we can divide both sides by two, s squared equals d squared divided by two, and then take the square root of both sides...