Final answer:
To find the dimensions of a rectangle with the smallest perimeter for a given area, we need to consider the formula for the perimeter of a rectangle which is P = 2(L + W). The dimensions of the rectangle with the smallest perimeter for an area of 1,331 m² are 77 m by 13 m.
Step-by-step explanation:
To find the dimensions of a rectangle with the smallest perimeter for a given area, we need to consider the formula for the perimeter of a rectangle which is P = 2(L + W), where L is the length and W is the width. Since we are given the area of the rectangle as 1,331 m², we can set up an equation to solve for the dimensions:
1,331 = L * W
Now let's find the values of L and W that minimize the perimeter:
- Start by finding the factors of 1,331: 1, 7, 11, 13, 77, 91, 121, 143, 847, and 1,331.
- Since we want the smallest perimeter, we need to find the pair of factors that gives the smallest sum. In this case, the pair is 77 and 13.
- Therefore, the dimensions of the rectangle are 77 m by 13 m.