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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

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 = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

a² - 3a - 25 = -4a + 5
a² - 3a - 25 - 5 = -4a
a² - 3a + 4a - 30 = 0
a² + a - 30 = 0

Next, factor the quadratic equation:

a² + a - 30 = 0
(a - 5)(a + 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 5) or (a + 6) must equal zero:

If (a - 5) = 0, a must equal 5
If (a + 6) = 0, a must equal -6

So the solution is that a = 5 or -6

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).

The volume of a cylinder is πr²h:

v = πr²h
v = π(1² x 5)
v = 5π

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.