Question

The area of a square is 72. what is the longest straight line that can be drawn between any two points of the square

Answer 1

The longest straight line that can be drawn between any two points of a square is the one that includes the points on the opposite corners of the squares. To determine the length of this straight line, we must first determine the length of the square's side. Since the area of the square can be calculated by taking the square of the side, then

s^2 = 72
s = 6 sqrt(2)

Then, using the Pythagorean theorem, we will find c (the longest side of straight line of the square) 

c^2 = a^2 + b^2

Upon substitution of the length of the square's side, we have
c^2 = (6 sqrt(2))^2 + (6 sqrt(2))^2
c^2 = 72+72
c = 72

The length of the longest line is 72.