# Math Help - EQ Triangle and square with same area

1. ## EQ Triangle and square with same area

The area of an equilateral triangle (A ft2) is equal to that of a square. What is the length of the diagonal of the square?

A. (2A) ft
B. A ft
C. (3A) ft
D. 2(A) ft
E. (5A) ft

I know how to get there, but not sure if it's a correct path (i.e. is there a better way to solve it.)

Forget the triangle, the area of both = A, and for the square A=s^2

Length of a diagonal of a square is S*2

Which we can see is A*2=(2A)

2. the diagonal of a square can be expressed d=(s^2+s^2)^(1/2) s is the square side
and s^2 is the area of the square so it is equal A

$d=\sqrt{s^2+s^2}=\sqrt{A+A}=\sqrt{2A}$

see this for more explanation

3. That's much more direct, thanks.