What is the length of a rectangle if the area is 24 meters squar and the height of 4 meters

We are given a rectangular yard with area of 24 square meters, and we are asked to find the possible perimeters.

Since the yard is a rectangle (a parallelogram with right angles), we can describe the dimensions as length and width. The area is given by A=lw and the perimeter by P=2l+2w.

Solving the equation of the area for the length l, noting that A=24, yields w=24/l  .

The domain for l and w is all positive reals.

(1) There are an infinite number of possible perimeters. Start with any positive real number l; then, w is given by 24/l, and the perimeter will be 2l+2w.

For example, if l=6, then w=4, and the perimeter is 20 meters. If l=13, then w=24/13, and the perimeter is 386/13.

Another example would be the following: l=sqrt(2), w=24/sqrt(2), P=26sqrt(2)  

(2) Possible perimeters with integer (whole number) sides:

1x24   P=50

2x12   P=28

3x8     P=22

4x6     P=20

These are the factorizations of 24.

(3) There is no largest perimeter, but there is a least perimeter.

We have P=2l+2(24/l) .

Using calculus, we can find the minimum perimeter to occur when the length and width are both equal to 2sqrt(6) .

This gives a perimeter of 8sqrt(6) approx 19.5959 .

(4) We can graph the possible perimeters: P=2l+48/l  

Step-by-step explanation:

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!