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.

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 9 x 1
a = 9

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

z² + z - 72 = 0
(z - 8)(z + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 8) or (z + 9) must equal zero:

If (z - 8) = 0, z must equal 8
If (z + 9) = 0, z must equal -9

So the solution is that z = 8 or -9

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 59° - 30° = 91°

So, d° = 30° + 91° = 121°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 59° = 121°

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