Answer:
The answer is below
Step-by-step explanation:
Mrs. Fielder decides to build a small snow shelter for her children to wait in before the school bus arrives in the morning. She has only enough wood for a total perimeter of 20 feet.
a. Make a table of all the whole number possibilities for the length and width of the shelter. Find the area of each shelter.
b. What dimensions should Mrs. Fielder choose to have the greatest area in her shelter?
c. What dimensions should Mrs. Fielder choose to have the least area in her shelter?
d. Township building codes require 3 square feet for each child in a snow shelter. Which shelter from part (a) will fit the most children? How many children is this? Explain your reasoning.
Solution:
a) Let W represent the width of the school shelter and let L represent the length of the school shelter. Therefore:
Perimeter of the school shelter = 2(length + breadth)
20 = 2(L + W)
L + W = 10
Also, the area of the school shelter = L * W
Length (ft) Width (ft) Area(ft²) = length * width
1 9 9
2 8 16
3 7 21
4 6 24
5 5 25
b) The shelter with a length of 5 ft and width of 5 ft has the largest area.
c) The shelter with a length of 1 ft and width of 9 ft has the least area.
d) The 4 by 6 ft shelter can hold 8 children (24 ft² / 3 ft² = 8) and the 5 by 5 ft shelter can hold 8 children with an extra space (25 ft² / 3 ft² = 8.33).
