# Thread: Finding Side's and diagonals with A

1. ## Finding Side's and diagonals with A

I'm going back to college after 5 years and am having a little trouble with geometry, one that i haven't been able to find an answer for is split into 3 parts;

A) What is the diagonal of a square who's side is A?

B) What is the side of a square whose diagonal is A?

C) Find the area of an equilateral triangle whose side is A.

I got the first one, but haven't been able to get the second ones. I assume I'm using the Pythagorean Theorem, but haven't been able to get it. If you could write out the steps it would help a lot. Thank you.

2. from A) itself you can get the answer for B),

in general let's take the diagonal of a square is $\displaystyle p$ and a side of a square is $\displaystyle q$, then the relationship between these two components can be expressed from the pythogoras theorem,

$\displaystyle q^2+q^2=p^2$
$\displaystyle 2q^2=p^2$
$\displaystyle \sqrt{2}q=p$ (since p, q are positive)

now substitute A with p or q according to the question asked

use the same theory to find the area of the triangle, for that you'll have to draw a line from one corner of the triangle which is perpendicular to the side which is facing that corner.

3. Hi gdied,
For C look up properties of equilateral triangles.Calculate area after finding the altitude