Question

Jack was given 400 m^2 of sod. What are the dimensions of the rectangular border, with the minimum perimeter, he could surround the sod with?

a) Length: 20 m, Width: 20 m
b) Length: 10 m, Width: 40 m
c) Length: 40 m, Width: 10 m
d) Length: 0 m, Width: 400 m"

Answer 1

The dimensions of the rectangular border, with the minimum perimeter, Jack could surround the sod with are: Length: 20 m, Width: 20 m

Step-by-step explanation:

The dimensions of the rectangular border, with the minimum perimeter, Jack could surround the sod with are:

1. Length: 20 m, Width: 20 m
2. Length: 10 m, Width: 40 m
3. Length: 40 m, Width: 10 m
4. Length: 0 m, Width: 400 m

The correct answer is option a) Length: 20 m, Width: 20 m. This is because the perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width. To minimize the perimeter, we want to minimize the sum of L and W. Since the area of the sod is given as 400 m^2, and the dimensions of the rectangular border must multiply to equal the area, we can set up the equation LW = 400. By trying out different combinations of L and W that satisfy this equation, we find that the dimensions with the minimum sum are L = 20 m and W = 20 m.