Perimeter and Area

[AdrienneNArndt]

How do you find the smallest possible area of a rectangle with the perimeter being 16 cm, and sides that are whole numbers? What is the greatest possible area?

 

[BigGlenntheHeavy]

Max. area of any rectangle is a square.

 

[Deleted member 4993]

How do you find the smallest possible area of a rectangle with the perimeter being 16 cm, and sides that are whole numbers? What is the greatest possible area?

1 x 7 will give you the minimum area with given constraints (assuming 0 is not allowed).

 

[pitoten]

Can you use calculus?


lw = Area
2l + 2w = 16

sub in l for w

-l^2 + 8l = A

dA/Dl = -2l + 8 = 0 at a max or min. l = 4 for the max. but I am not sure how to get the min. in this case

 

[TchrWill]

How do you find the smallest possible area of a rectangle with the perimeter being 16 cm, and sides that are whole numbers? What is the greatest possible area?

The smallest possible area derives from the rectangle of sides 1 and [16 - (2)1] = 7.

For a given perimeter, the square will result in the maximum area.
Given a square of X by X whose area is X^2.
Reducing one side by "a" and increasing the other side by "a", maintaining the perimeter constant, yields an area of (X - a)(X + a) = X^2 - a^2.
Thus, for a given perimeter, the square encloses the largest area.

 

[Denis]

If question is: find maximum area of a non-square rectangle with integer sides if perimeter = 4k + 2,
then area = k(k + 1)

Example: perimeter = 22
Then 4k + 2 = 22 : k = 5
Area = k(k + 1) = 5(6) = 30

In other words: closest possible to a square.

 

[Omar]

if two tiangles are simimar.the sides of the first one are 13,18 and 20.the smallest sides of the second tiangle is 22.find the perimerters of the second traingle.

 

[Omar]

Two polygons are similar. If the ratio perimeters is 4:7,what is the ratio of the corresponding sides?

 

[Denis]

Omar, start your own thread please.