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, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

4a - 2y = -8a + 6y - 1
4a = -8a + 6y - 1 + 2y
4a + 8a = 6y - 1 + 2y
12a = 8y - 1
a = \( \frac{8y - 1}{12} \)
a = \( \frac{8y}{12} \) + \( \frac{-1}{12} \)
a = \(\frac{2}{3}\)y - \(\frac{1}{12}\)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 8 as well and sum (Inside, Outside) to equal -6. For this problem, those two numbers are -4 and -2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 6y + 8
y² + (-4 - 2)y + (-4 x -2)
(y - 4)(y - 2)

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 7² + 1²
c² = 49 + 1
c² = 50
c = \( \sqrt{50} \)

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).