Algebra Demystified 2nd Ed

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?