Shamika is making cakes in the same shape, but different sizes, to sell at a school bake sale. She says that the perimeter for each cake is porportional to the length of one side. What shape are her cakes?

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Mathematics

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23 May, 20:51

Shamika is making cakes in the same shape, but different sizes, to sell at a school bake sale. She says that the perimeter for each cake is porportional to the length of one side. What shape are her cakes?

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Draven Hopkins · Answer 1

Answer: Square.

Shamika is making cakes that are of the same shape but they differ in sizes. According to her, the perimeter of one cake is proportional to one the side lengths.

If we consider a few basic shapes, we can think of a circle, a triangle, a square.

For circle, it cannot be true because it has no sides.

For this to be true for a triangle, the triangle must be equilateral.

However, a square is such a shape which has equal length of all the sides. So for squares of different sizes, the perimeter of each cake would be proportional to one of its side.

Perimeter of square = x + x + x + x = 4x

Therefore 4x/x = 4

A square of perimeter 4 will have a proportion of 1:4 from its length to perimeter.