-- All 4 sides of a square have equal length.
-- If the perimeter of a square is 24, then each side is (24/4) = 6 long.
-- When you cut the square along the diagonal, you have
a right triangle, with both legs 6 long.
The diagonal of the square is the hypotenuse of the triangle.
-- The length of the hypotenuse is the square root of
(one leg squared) plus (the other leg squared).
In this triangle, that's (6² + 6²) = (36 + 36) = 72 .
So the length of the hypotenuse is √72 .
Let's simplify that:
√72
= √(36 · 2)
= √36 · √2
= 6 · √2
There you have it . . . something worth remembering:
The length of the diagonal of a square is always
the length of one side, multiplied by √2 .
