Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 427

20

1

2

14

40 14

40 14

01440

0

2

2

=−

=−

=−

=−−

−=

BB

BB

BB

BB

()

()

()−−−−

=− ++

=− +

=− −

()

()(

14 40

01440

01440

010

2

2

2

BB

BB

BB

BB 4 4)

B − 10 = 0 B − 4 = 0

B = 10 B = 4

There are two triangles that satisfy the conditions. If the base is
10 inches, the height is 14 − 10 = 4 inches. If the base is 4 inches, the
height is 14 − 4 = 10 inches.

4. By the Pythagorean theorem, a^2 + b^2 = c^2. The hypotenuse is c, so c = 85.
   One leg is 71 longer than the other so a = b + 71 (b = a + 71 also works).
   The Pythagorean theorem becomes 85^2 = (b + 71)^2 + b^2.

85 71

7225 71 71

7225 142

222

2

2

=+ +

=+ ++

=+ +

()

()()

bb

bbb

bb 55041

7225 2 142 5041

02 142 2184

1

2

0

2

2

2

+

=++

=+ −

=

b

bb

bb

()^11

2

2 142 2184

071 1092

01384

2

2

()

()()

bb

bb

bb

+−

=+−

=− +

b − 13 = 0 b + 84 = 0 (This does not lead to a solution.)

b = 13

The shorter leg is 13 cm and the longer leg is 13 + 71 = 84 cm.