To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{9} \) = 3

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 3² + 3²
c² = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

-4a - 5 > \( \frac{a}{3} \)
3 x (-4a - 5) > a
(3 x -4a) + (3 x -5) > a
-12a - 15 > a
-12a - 15 - a > 0
-12a - a > 15
-13a > 15
a > \( \frac{15}{-13} \)
a > -1\(\frac{2}{13}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

-6x + 6 > -6 - 4x
-6x > -6 - 4x - 6
-6x + 4x > -6 - 6
-2x > -12
x > \( \frac{-12}{-2} \)
x > 6

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.