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:

z² + 4z + 3 = 0
(z + 1)(z + 3) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 1) or (z + 3) must equal zero:

If (z + 1) = 0, z must equal -1
If (z + 3) = 0, z must equal -3

So the solution is that z = -1 or -3

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 24 as well and sum (Inside, Outside) to equal -11. For this problem, those two numbers are -8 and -3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 11y + 24
y² + (-8 - 3)y + (-8 x -3)
(y - 8)(y - 3)

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

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD