418 algebra De mystif ieD
• Area of a circle A = πr^2 , where r is the circle’s radius.
• Volume of a rectangular box V = LWH, where L is the box’s length, W is
the box’s width, and H is the box’s height.
Most of the formulas above have at least one variable that is squared, which
will have us solving a quadratic equation. We usually have two solutions to this
equation but the geometric problem often only has one solution. We begin with
squares and other rectangles.
EXAMPLES
A square has a diameter of 50 cm. What is the length of each side?
Let x represent the length of each side.
50
x
x
FIGURE 11-3
The diagonal formula for a rectangle is DL^22 = + W^2. In this example,
D = 50, L = x, and W = x, so DL^22 = + W^2 becomes x^2 + x^2 = 50^2.
xx
x
x
x
xx
222
2
2
2
50
2 2500
2500
2
1250
1250 1250
+=
=
=
=
==( − iisnotasolution)
x
x
=⋅
=
25 2
25 2
2
Each side is 25 2 cm long.
EXAMPLES
A square has a diameter of 50 cm. What is the length of each side?
Let xxx represent the length of each side. represent the length of each side.
EXAMPLES
A square has a diameter of 50 cm. What is the length of each side?