Solve each problem. See Examples 3 and 4.
29.The John Hancock Center in Chicago has a rectangular base. The
length of the base measures 65 ft less than twice the width. The
perimeter of the base is 860 ft. What are the dimensions of the base?
30.The John Hancock Center (Exercise 29) tapers as it rises. The top
floor is rectangular and has perimeter 520 ft. The width of the top
floor measures 20 ft more than one-half its length. What are the
dimensions of the top floor?
76 CHAPTER 2 Linear Equations, Inequalities, and Applications
The
perimeter
of the
top
floor
is 520
ft.
The perimeter of the
base is 860 ft.
2 W – 65
L + 20
W
L
1
2
31.Grant Wood painted his most famous
work, American Gothic,in 1930 on com-
position board with perimeter 108.44 in.
If the painting is 5.54 in. taller than it is
wide, find the dimensions of the paint-
ing. (Source: The Gazette.)
32.The perimeter of a certain rectangle is
16 times the width. The length is 12 cm
more than the width. Find the length and
width of the rectangle.
W
W + 12
33.The Bermuda Triangle supposedly causes trouble for aircraft pilots. It has a perimeter of
3075 mi. The shortest side measures 75 mi less than the middle side, and the longest side
measures 375 mi more than the middle side. Find the lengths of the three sides.
34.The Vietnam Veterans Memorial in Washing-
ton, DC, is in the shape of two sides of an
isosceles triangle. If the two walls of equal
length were joined by a straight line of 438 ft,
the perimeter of the resulting triangle would
be 931.5 ft. Find the lengths of the two walls.
(Source: Pamphlet obtained at Vietnam
Veterans Memorial.)
35.The two companies with top revenues in the Fortune 500 list for 2009 were Exxon Mobil
and Wal-Mart. Their revenues together totaled $848.5 billion. Wal-Mart revenues were
$37.3 billion less than Exxon Mobil revenues. What were the revenues of each corpora-
tion? (Source:www.money.cnn.com)
36.Two of the longest-running Broadway shows
were Cats,which played from 1982 through
2000, and Les Misérables,which played from
1987 through 2003. Together, there were
14,165 performances of these two shows dur-
ing their Broadway runs. There were 805 fewer
performances of Les Misérablesthan of Cats.
How many performances were there of each
show? (Source:The Broadway League.)
438 ft
x x
American Gothicby Grant Wood. © Figge Art Museum/Estate of Nan
Wood Graham/ VAGA, NY
