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

p = x + y + z
p = 8cm + 14cm + 13cm = 35cm

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:

y² - 13y + 65 = 3y + 2
y² - 13y + 65 - 2 = 3y
y² - 13y - 3y + 63 = 0
y² - 16y + 63 = 0

Next, factor the quadratic equation:

y² - 16y + 63 = 0
(y - 7)(y - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 7) or (y - 9) must equal zero:

If (y - 7) = 0, y must equal 7
If (y - 9) = 0, y must equal 9

So the solution is that y = 7 or 9

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

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 < sign and the answer on the other.

-6b - 4 < -5 + b
-6b < -5 + b + 4
-6b - b < -5 + 4
-7b < -1
b < \( \frac{-1}{-7} \)
b < \(\frac{1}{7}\)

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 9 x 3 = \( \frac{27}{2} \) = 13\(\frac{1}{2}\)