Algebra Demystified 2nd Ed

Chapter 11 QuaDraTiC appliCaTionS 423

The hypotenuse of a right triangle is 34 feet. The sum of the lengths of the
two legs is 46 feet. Find the lengths of the legs. (The legs of a right triangle
are the sides that form the 90° angle.)

The sum of the lengths of the legs is 46 feet, so if we let a and b represent
the lengths of the legs, a + b = 46, so a = 46 – b. The hypotenuse is 34 feet
so if c is the length of the hypotenuse, then the formula a^2 + b^2 = c^2 becomes
(46 – b)^2 + b^2 = 34^2.

()

()()

46 34

46 46 1156

2116 92

22 2

2

2

−+=

−−+=

−++

bb

bbb

bbb^22

2

2

2

1156

292 2116 1156

292 960 0

1

2

292

=

−+ =

−+=

−

bb

bb

(bb++=

−+=

−−=

960 1

2

0

46 480 0

30 16 0

2

)()

()()

bb

bb

b − 30 = 0 b − 16 = 0

b = 30 b = 16

One leg is 30 feet long and the other is 46 – 30 = 16 feet long.

A can’s height is 4 inches and its volume is 28 in^3. What is the can’s
radius?

The volume formula for a right circular cylinder is V = or^2 h. The can’s volume
is 28 in^3 and its height is 4 inches, so V = or^2 h becomes 28 = or^2 (4).

28 4

28

4

28

4

1 493

2

2

=

=

=

≈

o

o

o

r

r

r

r

()

.

The can’s radius is about 1.493 inches.