no
No, not if they are squares.
Most shapes can have the same area and different perimeters. For example the right size square and circle will have the same are but they will have different perimeters. You can draw an infinite number of triangles with the same area but different perimeters. This is before we think about all the other shapes out there.
If, by changing the size of the squares you mean increasing the length of the side by some multiple, then the perimeter increases in direct proportion to the length of the side while the area increases in direct proportion to the square of the side. If, by changing the size of the the squares you mean increasing the length of the side from x units by some fixed small amount, dx units, then the perimeter will increase by 4*dx while the area will increase by 2*x*dx
Assume square A with side a; square B with side b. Perimeter of A is 4a; area of A is a2. Perimeter of B is 4b; area of B is b2. Given the ratio of the perimeters equals the ratio of the areas, then 4a/4b = a2/b2; a/b = a2/b2 By cross-multiplication we get: ab2 = a2b Dividing both sides by ab we get: b = a This tells us that squares whose ratio of their perimeters equals the ratio of their areas have equal-length sides. (Side a of Square A = side b of Square B.) This appears to show, if not prove, that there are not two different-size squares meeting the condition.
no
No, not if they are squares.
If a square's perimeter is 16.4 - it's sides are 4.1
There is no name for such shapes because "same size" is not defined. Does it mean same area? same perimeter? same major diagonal?
No, they have the same angles but may vary in size.
answer may vary depending on size of square
Assuming the 12 squares are the same size, three. And three more if you count different orientations (swapping length and breadth) as different rectangles.
Most shapes can have the same area and different perimeters. For example the right size square and circle will have the same are but they will have different perimeters. You can draw an infinite number of triangles with the same area but different perimeters. This is before we think about all the other shapes out there.
squares and rectanglesImproved Answer:-They are similar
If, by changing the size of the squares you mean increasing the length of the side by some multiple, then the perimeter increases in direct proportion to the length of the side while the area increases in direct proportion to the square of the side. If, by changing the size of the the squares you mean increasing the length of the side from x units by some fixed small amount, dx units, then the perimeter will increase by 4*dx while the area will increase by 2*x*dx
They may be of different sizes. Congruent figures have the same size.They may be of different sizes. Congruent figures have the same size.They may be of different sizes. Congruent figures have the same size.They may be of different sizes. Congruent figures have the same size.
Assume square A with side a; square B with side b. Perimeter of A is 4a; area of A is a2. Perimeter of B is 4b; area of B is b2. Given the ratio of the perimeters equals the ratio of the areas, then 4a/4b = a2/b2; a/b = a2/b2 By cross-multiplication we get: ab2 = a2b Dividing both sides by ab we get: b = a This tells us that squares whose ratio of their perimeters equals the ratio of their areas have equal-length sides. (Side a of Square A = side b of Square B.) This appears to show, if not prove, that there are not two different-size squares meeting the condition.