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

p = x + y + z
p = 12cm + 15cm + 10cm = 37cm

The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 5)(y + 6)
(y x y) + (y x 6) + (-5 x y) + (-5 x 6)
y² + 6y - 5y - 30
y² + y - 30

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -36 as well and sum (Inside, Outside) to equal -5. For this problem, those two numbers are -9 and 4. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 5y - 36
y² + (-9 + 4)y + (-9 x 4)
(y - 9)(y + 4)

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, \(c = \sqrt{a + b}\)