This is because 36 is a composite number.
A Prime number, p, has only the factorisation 1*p and so that is the only rectangle possible. But for a composite number there is at least one other factor q which may have a factor pair q' such that q*q' = p. q and q' could be the same if the number p was the square of q.
So then you have rectangles of size 1*p and q*q'.
ANY two positive numbers with a product of 36 will work. So, you can choose ANY real number (greater than zero), and then divide 36 by that number to get the other number.
Thee different rectangles with an area of 12 square units are 3 by 4, 2 by 6 and 1 by 12.
area = 144 square units perimeter = 48 units
Infinitely many. Select any number L, greater than sqrt(24) units an let B = 24/L. then the rectangle with sides measuring L and B will have an area of L*B = L*24/L = 24 square units. Also, B ≤ sqrt(24) ≤ L so that value of L gives a different rectangle. And, since there are infinitely many possible values for L, there are infinitely many possible rectangles.
Squares are rectangles. Draw a 2 unit square.
No solid figure has a surface area equal to its volume. That would not be possible as the units of measure are different.
Thee different rectangles with an area of 12 square units are 3 by 4, 2 by 6 and 1 by 12.
Area of a rectangle in square units = length*width
area = 144 square units perimeter = 48 units
There is no relationship between the perimeter and area of a rectangle. Knowing the perimeter, it's not possible to find the area. If you pick a number for the perimeter, there are an infinite number of rectangles with different areas that all have that perimeter. Knowing the area, it's not possible to find the perimeter. If you pick a number for the area, there are an infinite number of rectangles with different perimeters that all have that area.
3 or 6, depending on whether rectangles rotated through 90 degrees are counted as different. The rectangles are 1x12, 2x6 3x4 and their rotated versions: 4x3, 6x2 and 12x1.
Infinitely many. Select any number L, greater than sqrt(24) units an let B = 24/L. then the rectangle with sides measuring L and B will have an area of L*B = L*24/L = 24 square units. Also, B ≤ sqrt(24) ≤ L so that value of L gives a different rectangle. And, since there are infinitely many possible values for L, there are infinitely many possible rectangles.
Infinitely many.
Squares are rectangles. Draw a 2 unit square.
1x16 2x8 and 4x4
Infinitely many.Let L be any number greater than or equal to sqrt(24) units.and let B = 24/LThen the area of the rectangle with length L units and breadth B units will beL * B = L *24/L = 24 square units.Since there are infinitely many possible values for L, there are infinitely many possible answers to the question.
No solid figure has a surface area equal to its volume. That would not be possible as the units of measure are different.
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