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 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:

b² - 3b + 8 = 3b + 3
b² - 3b + 8 - 3 = 3b
b² - 3b - 3b + 5 = 0
b² - 6b + 5 = 0

Next, factor the quadratic equation:

b² - 6b + 5 = 0
(b - 1)(b - 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 1) or (b - 5) must equal zero:

If (b - 1) = 0, b must equal 1
If (b - 5) = 0, b must equal 5

So the solution is that b = 1 or 5

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 9 + 5 + 9 + 3
p = 26

An equation is two expressions separated by an equal sign. The key to solving equations is to 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.

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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

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 = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)