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 = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

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 = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)

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.

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

c² = a² + b²
c² = 1² + 9²
c² = 1 + 81
c² = 82
c = \( \sqrt{82} \)

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.

(5a)(9ab) + (9a²)(6b)
(5 x 9)(a x a x b) + (9 x 6)(a² x b)
(45)(a¹⁺¹ x b) + (54)(a²b)
45a²b + 54a²b
99a²b

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 equal sign and the answer on the other.

8b - 1 = \( \frac{b}{-2} \)
-2 x (8b - 1) = b
(-2 x 8b) + (-2 x -1) = b
-16b + 2 = b
-16b + 2 - b = 0
-16b - b = -2
-17b = -2
b = \( \frac{-2}{-17} \)
b = \(\frac{2}{17}\)