yes
Yes, if the perimeters are the same, then both of them have side = perimeter / 4. And of course the angles are all 90°, since they are squares.
MOst of it
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.
Because the area is different than the perimeters
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.
they are different because perimeter is the out side of the shape and area is inside of the shape.
That depends on the rectangle! You can have different rectangles with the same area, but with different perimeters.
If they have the same area.
No, they are not equal. Say a rectangle is 3 x 2 = 6 sq in area Say another is 6 x 1 = 6 sq in area perimeter of first one is 2L + 2B = 10 perimeter of second one is 2L + 2B = 14
You can come up with the same number (4 x 4) but you can't come up with the same units.
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.
That depends on the exact shape. For the same area, you can have different perimeters, depending on the shape.