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# Can a rectangle's area be the same as the perimeter?

To answer that question, look at the formulas for both Let's take a rectangle with length L and width W. The area is LW and the perimeter is 2L+2W

So can LW=2L+2W

Solve for L LW/2=L+W 1/2L(w-2)=w L=(2w)/(W-2)

This tells us the answer is YES. But it also tells us W must be greater than 2. Try W=3, this gives us L= 6/1=6 So look at a 6x3 rectangle Area is 18 and perimeter is 12+6=18

True, but there is an important caveat. The numbers, for the area and perimeter, can be the same but the two cannot be the same. The simple reason is that the area will be in square units whereas the perimeter will be in linear units. The consequnce of this is that if the units of measurement are changed (eg from centimetres to metres, or inches) the equality in numbers will no longer hold. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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