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

p = x + y + z
p = 13cm + 14cm + 14cm = 41cm

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

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

An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

x² + 2x - 63 = 0
(x - 7)(x + 9) = 0

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

If (x - 7) = 0, x must equal 7
If (x + 9) = 0, x must equal -9

So the solution is that x = 7 or -9