Cristina has 16 square feet of material to make a rectangular quilt. She wants the quilt to have the least possible(minimum) perimeter. If Cristina uses all 16 square feet, what dimensions should she use for the quilt?

4 by 4 feet

4 by 4 feet

I don't have a answer but I have the same question for my homework and i am stuck on it.

To find the dimensions that would minimize the perimeter of the quilt, we need to determine the dimensions that would maximize the area while using all 16 square feet of material.

Let's suppose the length of the rectangular quilt is 'l' and the width is 'w'.

The area of a rectangle is given by the formula: Area = length * width.

In this case, the area of the quilt should be equal to 16 square feet, so we can write the equation: l * w = 16.

Now, we want to minimize the perimeter, which is given by the formula: Perimeter = 2 * (length + width).

To minimize the perimeter, we need to find the values of 'l' and 'w' that satisfy the area equation and give the smallest possible value for the perimeter.

To solve this problem, we can try different combinations of length and width that multiply to give 16, while calculating the corresponding perimeters.

Let's start by listing all the possible pairs of factors of 16:

1 * 16 = 16
2 * 8 = 16
4 * 4 = 16
8 * 2 = 16
16 * 1 = 16

Now we'll calculate the perimeters for each pair:

1 * 16 -> Perimeter = 2 * (1+16) = 34
2 * 8 -> Perimeter = 2 * (2+8) = 20
4 * 4 -> Perimeter = 2 * (4+4) = 16
8 * 2 -> Perimeter = 2 * (8+2) = 20
16 * 1 -> Perimeter = 2 * (16+1) = 34

By comparing the perimeters, we can see that when the dimensions are 4 feet by 4 feet, the perimeter is minimized at 16 feet. Therefore, Cristina should use a rectangular quilt with dimensions of 4 feet by 4 feet to use all 16 square feet of material and have the smallest possible perimeter.