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Can 2 different size squares have the same perimeter?
no
Can two different size square have the same perimeter explian?
No, not if they are squares.
What shapes have the same perimeter but different areas?
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.
How does changing the size of the squares affect the perimeter and area of the figure?
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
What are two different size squares that the ratio of their perimeters is the same as the ratio of their areas?
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.
