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if a rug's perimeter is 17cm and the area is 13cm, what are the reasurments for the length and width?

Are you sure you copied this problem correctly?

A rug with a perimeter of 17 cm wouldn't be large enough to hold my big toe.

this is copied correctly. the teacher wanted to keep it simple

Your teacher should have stated that the area is 13 cm^2.
If your teacher tried to make it simple, then he/she did not do such a good job.
I did it by algebra and it led to a quadratic equation.

length - x
width - y
2x + 2y = 17
x + y = 8.5
also xy = 13, so y = 13/x

x + 13/x = 8.5
x^2 - 8.5x + 13 = 0
2x^2 - 17x + 26 = 0
(x-2)(2x - 13) = 0
x = 2 or x = 6.5
if x = 2 , then y = 6.5
if x = 6.5, then y = 2

so the "rug" is 2 cm by 6.5 cm, and as Ms Sue noted, probably just big enough to fit into a doll house.

I have a 4th grade "guess" at that answer is rather stretching it.

That is not 4th grade homework

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