The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 5cm + 11cm + 5cm = 21cm

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(4a)(2ab) - (8a²)(8b)
(4 x 2)(a x a x b) - (8 x 8)(a² x b)
(8)(a¹⁺¹ x b) - (64)(a²b)
8a²b - 64a²b
-56a²b

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\( \sqrt{2} \)

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

x² - x - 56 = 0
(x + 7)(x - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 7) or (x - 8) must equal zero:

If (x + 7) = 0, x must equal -7
If (x - 8) = 0, x must equal 8

So the solution is that x = -7 or 8