How would I find the max area of a rectangle, if i were giving 300m of rope ?

Question

I really don't understand how to find the max area, i checked in my textbook but it dosen't say anything about it

The answer in the text book is 11 250m squared, how would I get that ??

The answer in the text book is 11 250m squared, how would I get that ??

Answer 1

The area of a rectangle of constant perimeter is maximized when the rectangle is a square.

If you have 300m of rope to form the perimeter of your shape, your square would be 300m/4 = 75m on a side, with an area of 5,625 m^2.

You can rigorously prove that this is the case, with calculus.

Let's say you are going to make a rectangle with perimeter 300, and its width is w. Using the forumula for perimeter of a rectangle:

p = 2w + 2h
300 = 2w + 2h
h = 150 - w

Now, recall that the area of a rectangle is w*h, and substitute the above:

a = w * h
a = w * (150 - w)
a = 150w - w^2

To find which width gives the maximum area, take the derivative with respect to w, and set it equal to zero:

da/dw = 0
d(150w - w^2)/dw = 0
150 - 2w = 0
2w = 150
w = 75

The maximum area of your rectangle occurs when w=75

Answer 2

the maximum area of a rectange is a sqare.

because you're given 300m of rope, you want to figure out how you can make that square. each side would have 75 m. (divide 300 by 4)

multiply 75 by 75, and you get 5625m^2.

*if you want to check your answer, you can use extremes, because they make it clearer to see the difference. if you had a rectangle with a width of 1 and a length of 149, your area would be just 149. you want the greatest possible numbers of both length AND width.

Answer 3

the area is countless * the area of a rectangle might want to be discovered through multiplying the bottom circumstances the finished. * If a rectangle has a base of length 6 inches and a excellent of four inches, its section is 6*4=24 sq. inches

Answer 4

use a square so
p=2l+2w
square so legnth and width are the same so
p=4l
area=l*l so
(p/4)^2=area
(300/4)^2=A
75^2=A
5625=A

Answer 5

it would be a 75 by 75 square

75ft+75ft+75ft+75ft=300ft

area 75ft*75ft= 5625ft^2