Two similar polygons have areas of 16 square inches and 64 square inches. The ratio of a pair of corresponding sides is 1/4.
True
False
its true?
No, it's not.
With similar figures, the ratio of areas is the square of the ratio of sides (or other linear dimensions such as the apothem, height, etc.)
Similarly, the ratio of volumes of similar solids varies with the cubes of the linear dimensions.
Here, the ratio of area is 64/16=4, and 4 is the square of 2. So the ratio of the sides is....
False
True.
The ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding sides. In this case, the ratio of the areas is 16/64 = 1/4.
The square root of 1/4 is 1/2, which is equal to the ratio of the sides. Therefore, the ratio of the corresponding sides of the two polygons is indeed 1/4.
To determine if the statement is true or false, we need to compare the ratios of the areas of the two polygons and the ratios of their corresponding sides.
Given that the ratio of the areas of the two polygons is 16 square inches to 64 square inches, we can simplify this ratio by dividing both sides by 16. This gives us 1 square inch to 4 square inches.
Given that the ratio of the corresponding sides is 1/4, we can see that the ratio of the areas (1 square inch to 4 square inches) corresponds exactly to the ratio of the sides. This means that the two polygons are similar.
Therefore, the statement is TRUE.