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Is there a relationship between area and perimeter of a rectangle and Why?
Yes, there is a relationship between the area and perimeter of a rectangle, although they measure different aspects. The area is calculated by multiplying the length by the width, while the perimeter is the sum of all sides, given by the formula ( P = 2(l + w) ). As the dimensions of a rectangle change, both area and perimeter can increase or decrease, but they do not have a direct proportional relationship; for instance, a rectangle can have the same perimeter but different areas depending on its length and width.
What is the perimeter of a rectangle has an area of 5cm square?
The perimeter of a rectangle cannot be determined with the area alone as the lengths could vary. For example, the perimeter of the rectangle could be 12 (1 and 5) or 9 (2 and 2.5). For both cases, the area is still 5cm2, but the length can still change to result in different results.
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.
Do all rectangles with the same area have the same perimeter?
No, rectangles with the same area do not necessarily have the same perimeter. The perimeter of a rectangle depends on both its length and width, while the area is simply the product of these two dimensions. For instance, a rectangle measuring 2 units by 6 units has an area of 12 square units and a perimeter of 16 units, while a rectangle measuring 3 units by 4 units also has an area of 12 square units but a perimeter of 14 units. Thus, different length and width combinations can yield the same area but different perimeters.
Why is finding the perimeter of a triangle related to finding the perimeter of a rectangle?
It is not in all but a trivial sense - that they are both to do with finding the perimeter!
Can a rectangle have a greater perimeter and also have a greater area?
Of course, a rectangle can have a greater perimeter and a greater area. Simply double all the sides: the perimeter is doubled and the area is quadrupled - both bigger than they were.
Can a rectangle have a greater perimeter than another one but have a greater area too?
yes it can; a rectangle 5 by 2 has perimeter 14 and area 10 for example; a rectangle 10 by 2 has perimeter 24 and area 20, both greater.
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
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.
Two polygons that have the same perimeter but a different area?
For example, a 1x15 rectangle and a 2x14 rectangle. They both have perimeter of 32, but they have areas of 15 and 28, respectively.
If a rectangle has the same area does it have the same perimeter?
No.For example, a 1 metre * 72 metre rectangle and a 8 metre * 9 metre rectangle both have areas of 72 square metres. But the perimeter of the first is 146 metres while that of the second is 34 metres.
What is the perimeter of a rectangle has an area of 5cm square?
The perimeter of a rectangle cannot be determined with the area alone as the lengths could vary. For example, the perimeter of the rectangle could be 12 (1 and 5) or 9 (2 and 2.5). For both cases, the area is still 5cm2, but the length can still change to result in different results.
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.
What is the perimeter of a rectangle that has an area of 432 feet?
Ah, what a lovely question! To find the perimeter of a rectangle, we need to know both the length and width. Since the area is 432 square feet, we can find the dimensions by factoring 432 into pairs of numbers until we find a pair that could be the length and width of the rectangle. Once we have the dimensions, we can simply add up all the sides to find the perimeter.
Can rectangles with the same perimeter have different areas?
Yes. Say there are two rectangles, both with perimeter of 20. One of the rectangles is a 2 by 8 rectangle. The area of this rectangle is 2 x 8 which is 16. The other rectangle is a 4 by 6 rectangle. It has an area of 4 x 6 which is 24.
How are the perimeter and area of a rectangle affected if the legth and the width are changed proportionally?
If the length and width of a rectangle are both multiplied by K, then the originalperimeter is multiplied by K, and the area is multiplied by K2 .
Do all rectangles with the same area have the same perimeter?
No, rectangles with the same area do not necessarily have the same perimeter. The perimeter of a rectangle depends on both its length and width, while the area is simply the product of these two dimensions. For instance, a rectangle measuring 2 units by 6 units has an area of 12 square units and a perimeter of 16 units, while a rectangle measuring 3 units by 4 units also has an area of 12 square units but a perimeter of 14 units. Thus, different length and width combinations can yield the same area but different perimeters.
