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Technically, no because a perimeter is a linear measure and an area is a square measure. However, there are infinitely many rectangles such that the NUMERICAL VALUE of their perimeter is the same as the NUMERICAL value of their area.
Select any number y greater than or equal to 4.
let x = 2*y/(y-2)
Consider the rectangle with dimensions width x and length y.
Its area is x*y = [2*y/(y-2)]*y = 2y2/(y-2) square units.
Its perimeter is 2(x+y) = 2*[(2y/(y-2) + y] = 2/(y-2)*[2y+y*(y-2)]
= 2/(y-2)*[2y+y2-2y] = 2/(y-2)*y2 = 2y2/(y-2) units
Since y is an arbitrary number greater than 4, there are infinitely many choices for y giving rise to infinitely many shapes. The one with the smallest y: y = 4 is actually a square - with sides of 4 units and perimeter/area = 16.
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If same area in a rectangle does that mean same perimeter?
No. For example, a 4x1 rectangle will have an area of 4 and a perimeter of 10. A 2x2 rectangle will have the same area of 4, but a perimeter of 8.
The area of a rectangle is 100 inches the perimeter is 40 a second rectangle has the same area but a different perimeter. Is the second rectangle a square?
the area of a rectangleis 100 square inches. The perimeter of the rectangle is 40 inches. A second rectangle has the same area but a different perimeter. Is the secind rectangle a square? Explain why or why not.
The area of a rectangle is 100 square inches The perimeter of the rectangle is 40 inches A second rectangle has the same area but a different perimeter Is the second rectangle a square?
yes
Does a equable rectangle have the same area and perimeter?
yes
What type of rectangle has the smallest perimeter for the same area?
A square.
