3. A farmer wants to build a sheepyard that is 120 square metre in area. Suggest three different rectangular shapes for him. Draw them. Also write how much fence he needs for each yard. Write, which rectangular shape of yours uses the least amount of fence?
Answers
Least amount of fence is when Length & breadth are equal or closest to each other
Step-by-step explanation:
Area = Length * Breadth
Area = 120
120 = 12 * 10 = 15 * 8 = 20 * 6 = 24 * 5 = 30 * 4 = 60 * 2 = 120 * 1
Fence Required = Perimeter
Perimeter = 2 ( Length + Breadth)
Length Breadth Perimeter
12 10 44
15 8 46
20 6 52
24 5 58
30 4 68
60 2 124
120 1 242
For the integral values least amount of fence when 12 * 10
Least Difference between Length & Breadth
for non integral value Length = Breadth = √120 will give least fence
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Answer:
Shape a. 120m² (Length 12m and width 10m) uses the least amount of fence.
Step-by-step explanation:
A farmer wants to build a sheep yard that is 120 square meter in area.
Area = Length × width
Three different rectangular shapes would be
Area = L × w
a. 120 m² = 12m × 10m
b. 120 m² = 15m × 8m
c. 120 m² = 20m × 6m
To calculate the length of fence that he need for each yard, we will calculate perimeter of the yard.
Perimeter = 2(Length + width)
a. Perimeter = 2(12 + 10)
= 44 meter
b. Perimeter = 2(15 + 8)
= 46 meter
c. Perimeter = 2(20 + 6)
= 52 meter
Shape a. 120m² (Length 12m and width 10m) uses the least amount of fence.
