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Preimeter is a measure of length, area ... well, of area. You can't really compare the perimeter and the area. If both are equal in one unit (like centimeter vs. square centimeter), they won't be equal in another unit (like meters and square meters).
Anyway, to be numerically equal, you must solve the equation area = perimeter. Assuming dimensions of a times b, the equation becomes:
ab = 2(a+b).
Solving for a:
ab = 2a + 2b
ab - 2a = 2b
a(b-2) = 2b
a = 2b / (b-2)
With this last equation, you can substitute any value for b, and get the corresponding value for a. It seems there are infinitely many solutions.
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How many rectangles have the same area and perimeter of 18?
thare is only 1 differint rectangles
Why does rectangles have the same area and perimeter?
they dont
How many rectangles have the same area as their perimeter?
The only one I can think of is a square, where Length=Width=4.
How would finding the area of a square be the as finding the area of a rectangle?
Squares are rectangles so the formula for area will stay the same.
How many rectangles have the same area but different perimeters?
Infinitely many. Suppose the area of the rectangle is 100. We could create rectangles of different areas: 100x1 50x2 25x4 20x5 10x10 However, the side lengths need not be integers, which is why we can create infinitely many rectangles. Generally, if A is the area of the rectangle, and L, L/A are its dimensions, then the amount 2(L + (L/A)) can range from a given amount (min. occurs at L = sqrt(A), perimeter = 4sqrt(A)) to infinity.
