A rectangle has a perimeter of 26 units and an area more than 30 square units. Write an inequality use n as the variable.

Answer 1

2x+2y=26

x+y=13

xy>30

x=5; y=8

4 9

6 7 etc

Answer 2

Hi Kimberly,

Rectangles have a length and a width. The perimeter of a rectangle is found by adding up the four sides, which means

Perimeter = length + length + width + width

Or we could rewrite it

Perimeter = 2 * length + 2 * width

Let n be the length of the rectangle. Then since the perimeter is 26 we have

26 = 2 * n + 2 * width. Now subtract the 2 * n from each side:

26 - 2n = 2 * width. Now divide both sides by 2:

(26 - 2n) / 2 = width. The left hand side simplifies to:

13 - n = width.

The area of a rectangle is its length * width. We are told that:

Area > 30. This means:

length * width > 30. We can now write each piece of the left hand side using only n:

n * (13 - n) > 30.

Note that n has to be between 0 and 13, otherwise we’ll get either a length or a width that is zero or negative and makes no sense.

Please let me know if I can be more helpful, thanks!

Joe