# what is the area of a rectangle if the perimeter is 80no

embizze | High School Teacher | (Level 1) Educator Emeritus

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What is the area of a rectangle with perimeter of 80 units?

If you try a few possible side lengths, you will find that there are many possible areas. For instance, if the rectangle is a square with side length 20 (note that the perimeter is 80), then the area is 400. If the length is 30 then the width is 10 and the area is 300, etc...

Let x be the length of the rectangle. Then the width is 40-x. (x+x+40-x+40-x=80).

Then the area is given by x(40-x) or -x^2+40x. The bounds on x are 0<x<40, so the bound on the area is `0<a<=400` .

elizabeth-newton | Student, Grade 9 | eNotes Newbie

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You would find the length of each side. You would do 80 divided by 4 because there are four sides on a rectangle. The answer is 20.

The formula for perimeter is L x W= P (length times width equals perimeter)

Therefore you would do 20 x 20 and that would come out to 400.