A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.

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

c² = a² + b²
c² = 2² + 2²
c² = 4 + 4
c² = 8
c = \( \sqrt{8} \)

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 = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

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 = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

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:

z² - 11z + 5 = -5z - 3
z² - 11z + 5 + 3 = -5z
z² - 11z + 5z + 8 = 0
z² - 6z + 8 = 0

Next, factor the quadratic equation:

z² - 6z + 8 = 0
(z - 2)(z - 4) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 2) or (z - 4) must equal zero:

If (z - 2) = 0, z must equal 2
If (z - 4) = 0, z must equal 4

So the solution is that z = 2 or 4