The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

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

p = x + y + z
p = 12cm + 9cm + 5cm = 26cm

To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

-9c - 9y = 2c - 7y + 9
-9c = 2c - 7y + 9 + 9y
-9c - 2c = -7y + 9 + 9y
-11c = 2y + 9
c = \( \frac{2y + 9}{-11} \)
c = \( \frac{2y}{-11} \) + \( \frac{9}{-11} \)
c = -\(\frac{2}{11}\)y - \(\frac{9}{11}\)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).