Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 419

A rectangle is 1 inch longer than it is wide. Its diameter is 5 inches. What are
its dimensions?

5

W

W + 1

FIGURE 11-4

The diagonal formula for a rectangle is D^2 = L^2 + W^2. In this example, D = 5
and L = W + 1. DL^22 =  + W^2 becomes 5^2 = (W + 1)^2 + W^2.

51

25 11

25 21

25 2

222

2

22

2

=++

=+ ++

=+++

=

()

()()

WW

WW W

WWW

W +++

=+−

=+−

=+−

=

21

02 224

1

2

0 1

2

2224

012

0

2

2

2

W

WW

WW

WW

() ()

(()WW−+ 34 ()

W − 3 = 0 W + 4 = 0

W = 3 W = − 4 (not a solution)

The width is 3 inches in the length is 3 + 1 = 4 inches.

PRACTICE

1. The diameter of a square is 60 feet. What is the length of its sides?


2. A rectangle has one side 14 cm longer than the other. Its diameter is
   34 cm. What are its dimensions?


3. The length of a rectangle is 7 inches more than its width. The diagonal
   is 17 inches. What are its dimensions?

PRACTICE

1. The diameter of a square is 60 feet. What is the length of its sides?


2. A rectangle has one side 14 cm longer than the other. Its diameter is

PRACTICE

1. The diameter of a square is 60 feet. What is the length of its sides?