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

a = ½bh
a = ½ x 5 x 2 = \( \frac{10}{2} \) = 5

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

-3b - 4x = 9b - 6x + 4
-3b = 9b - 6x + 4 + 4x
-3b - 9b = -6x + 4 + 4x
-12b = -2x + 4
b = \( \frac{-2x + 4}{-12} \)
b = \( \frac{-2x}{-12} \) + \( \frac{4}{-12} \)
b = \(\frac{1}{6}\)x - \(\frac{1}{3}\)

A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).