0
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.
Add your answer:
Earn +20 pts
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.
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
In general describe the rectangle that has the least area for a fixed perimeter?
For a fixed perimeter, the area will always be the same, regardless of how you describe the rectangle.
Does a equable rectangle have the same area and perimeter?
yes
Do figures with the same perimeter have the same area?
not necessarily. take the example of a 3x3 square and a 4x2 rectangle. Both have a perimeter of 12. but the square has an area of 9 and the rectangle has an area of 8.
Show you 2 rectanglesthat have the same area and different perimeter?
A rectangle with sides of 1cm and 6cm has an area of 6 cm2 and a perimeter of 14 cm. A rectangle with sides of 2cm and 3cm has the same area but its perimeter is 10 cm.
What type of rectangle has the smallest perimeter for the same area?
A square.
How can the perimeter stay the same and the area change?
4x4 square: perimeter - 16 area - 16 6x2 rectangle perimeter - 16 area - 12
Can a rectangles perimeter be the same as the area?
Yes, it can because a 3 by 6 rectangle has the perimeter of 18 and has the area of 18! :)
If two rectangle have the same area must they have the same perimeter?
Not always because a 2 by 12 rectangle will have the same area as a 4 by 6 rectangle but they both will have different perimeters.
Can two parallelograms have the same perimeter but different areas?
yes, for example: a 4 by 5 rectangle has an area of 20 and a perimeter of 18 a 2 by 7 rectangle has an area of 14 and a perimeter of 18 they both have a perimeter of 18
