Among all rectangles that have a perimeter of 20 ft, find the dimensions of the with the largest area?

Question

Please show work!

Answer 1

Let x ft be the length of one side of the rectangle.
Then the length of the adjacent side is 10-x ft.
The area is x(10-x) = 10x - x^2 sq.ft.
10x - x^2 can be written 25 - (x-5)^2.
The term (x-5)^2 is a square, and is therefore never negative.
The maximum area is therefore 25 sq.ft., and arises when x-5 = 0 or when x=5.
The lengths of the two sides are therefore both 5ft, and as previous answers have said, the largest area is when the rectangle is a square.

Answer 2

This works really well if you have graph paper. Then you can actually draw all the rectangles with a perimeter of 20. Example; 1+1+9+9 = 20. 2+2+8+8 = 20. There will be 5 rectangles in all. Then when you multiply the length times the width you will also have the areas. 9 x1 =9 sq.ft. 2x8=16sq.ft. and so on. When you get to 5+5+5+5, you will have a perimeter of 20 and an area of 25sq.ft. This is your answer.

Answer 3

A rectangle will have its largest area in a square form. In this case a square with dimensions of 5x5 can be formed. (20/4 =5). Is this some kind of homework? Honestly there isn't much work to show though, as there are only a proven fact and a simple equation.

Answer 4

between all rectangles with an analogous parimeter, the only with the biggest area is the sq.. so which you will would desire to discover the size of a sq. with perimeter of 20 ft. If s is the size of the two facets of a sq., then it particularly is perimter is 4s. subsequently, 4s = 20 So, s = 20/4 = 5 the size of the sq. are 4 facets each and each 5 ft long, and it particularly is area is 5x5=25 squareft.

Answer 5

First find a square that has same perimeter, i.e.each side =5 ft.
Now if yo need a rectangle with maximum area, the length has to be closest to the side of the square. It depends if you need the area to be a natural number or it can be in fraction.
If the area has to natural number you may pick a rectangle with length=(5+1) ft. and width=(5-1) ft
Area= 6x4=24 sq.ft.
If you need answer in decimals you may pick a rectangle with length=(5+0.1) ft and width=(5-0.1) ft
Area will be= 5.1x4.9 = 24.99 sq ft.
I hope this answers your question.

Answer 6

Area = length X width

perimeter = 2 X length + 2 X width

So, it does not matter how you parse the perimeter; if you have a certain perimeter, you have a certain area.

Answer 7

It would probably be the perfect rectangle, a square whose sides =5 thus an area of 25ft squared.