Comfortable Horse Stalls
The plan for a new hare includes standard, rectangular horie stalls. The architect is sure that this will
provide the most comfort for your horse because it is the greatest ares for the stall. Is that correct?
How can you investigate to find out?
The budget for your new barn allows for a horse stall with a total perimeter of 44 feet. The stall in the
current plans is 10-foot by 12-foot, an industry standard.
1. a. Explore the options for the dimensions of the stall by completing the table. Then sketch each
stall on the coordinate plane as shown for the 10-foot by 12-foot stall.
Length (in feet) Width (in feet)
S
6
7
8
*
10
11
12
197
16
14
18
12
Perimeter
419
48
47
46
45
44
43
42
Area
85
96
2.10
w12
e. Solve the perimeter equation for length (.
105
112
117
120
121
34
16
12
4
0
8
10
b. From your table, does a 10-foot by 12-foot stall provide the most area? If not, which size stall does?
11-foot by 11-foot
2. Now investigate this problem algebraically and graphically.
a. Write an equation for 4, the area of the stall, in terms of length and width w.
b. Write an equation for the perimeter of the stall in terms of length and width w,
given that the perimeter is 44 feet.
d. Substitute the expression for length found in part (b) into your equation for area found
in part (a). Write your new equation 4(w).
16
Use a graphing calculator to graph the area function 4(w) changing the viewing window
until you see the maximum of the function. Explain what the function represents in terms
of the domain and range.
Using the maximum feature on your calculator, what is the maximum area? What
dimensions correspond to this area? Does this agree with your table?
3. What rectangular shape has the largest area for a fixed perimeter? Why might barn owners
choose to build standard 10-foot by 12-foot harm stalls instead of stalls in this shape?


i need help please help