# Applications and Modeling with Linear Equations

SECTION 1.2 Applications and Modeling with Linear Equations i 93
13. P€I‘il?’l£?l.’t’.r‘ of (1 Plot of Land The perimeter of a triangular plot of land is 2400 ft..
The longest side is 200 ft less than twice the shortest. The middle side is 200 ft less
than the longest side. Find the lengths of the three sides of the triangular plot.
‘u J H 021\$‘ 14. Worlrl Lrrrgest Irre Crcarn Cake The world’s largest ice cream cake, made at the
y ~ 5 H T” ‘ 0 Baxy ice cream factory in Beijing, China, on January 16, 2006, had length 5.9 ft
r i t‘ ” “is [’’l {»j*-r,i=. greater than its width. Its perimeter was 51 ft. What were the length and width of this
ft,‘ xii 8-ton cake‘? (Sr;-mrces: www.chinadaily.coni.cn, wwwfoodmallorg)
15. Wnrld’s Sntrrllesf Qurnn. The world’s smallest Quran, published in Cairo, Egypt,
J in 1982 has width 0.42 cm shorter than its length. The book’s perimeter is 5.96 cm.
-3;” __. What are the width and length of this Quran, in centimeters? (_SourCe.‘ www.guin-
if nessworldrecordscom)
if 16. C__vIin.der Dr’mensr’on..s’ A right circular cylinder has radius 6 in. and volume
What is its height? (In the figure, I1 = height.)
17. Rec:_ircliri.g Bin Dii:iensrTor1s A recycling bin is in the shape of a rectangular box.
Find the height of the box if its length is 18 ft, its width is 8 ft, and its surface area is
496 ftz. (In the figure, 12 = height. Assume that the given surface area includes that
of the top lid of the box.)
18 ft 8 ft
CARGO i ,1
18. Crmcept C heck Which one or more of the following cannot be a correct equation
to solve a geometry problem, if x represents the length of a rectangle? (Hz’nt.’ Solve
each equation and consider the solution.)
A. 2x+2(.r-l)=14 B. -2,r+7(5-x)=52
C. 5(x-l-2)+5x=lo D. 2.:+2(x-3)=22
Solve each. problem. See Example 2. 0
19. Distance to an Appnintrnent Margaret 1,, t d
drove to a business appointment at
50 mph. Her average speed on the return Mflrllillg
trip was 40 mph. The return trip took ,_‘-, hr Afternoon
longer because of heavy traffic. How far
9 ‘d she travel to the appointment?
‘ram.-c between (..‘i’ti’es On a vacation, r t d
wyn averaged 50 mph traveling from
Denver to Minneapolis. Returning by 21 Going
different route that covered the same nurn- Rem in
her of miles, he averaged 55 mph. What is m g x
the distance between the two cities if his
total traveling time was 32 hr?