The ratio of the sides of two squares is 3:8. Find the ratio of the perimeters of the two squares. Find the ratio of the areas of the two squares.
since the lengths are 3:8,
perimeter, also a length, is 3:8
area = length*length = 3^2:8^2 = 9:64
thank you Steve
Let the side of square be 3x and 5x
So Area =9x
2
and 25x
2
Ratio =
25x
2
9x
2
=9:25
To find the ratio of the perimeters of the two squares, we need to determine the values of the side lengths. Let's assume that the side length of the first square is 3x, where x is a constant. Therefore, the side length of the second square would be 8x.
The perimeter of a square is given by the formula P = 4s, where P represents the perimeter and s represents the side length.
For the first square:
Perimeter = 4 * side length = 4 * 3x = 12x
For the second square:
Perimeter = 4 * side length = 4 * 8x = 32x
Therefore, the ratio of the perimeters is 12x:32x. We can simplify this ratio by dividing both numerator and denominator by 4x.
So, the simplified ratio of the perimeters is 3:8.
Now, let's find the ratio of the areas of the two squares. The area of a square is given by the formula A = s^2, where A represents the area and s represents the side length.
For the first square:
Area = side length^2 = (3x)^2 = 9x^2
For the second square:
Area = side length^2 = (8x)^2 = 64x^2
Therefore, the ratio of the areas is 9x^2:64x^2. We can further simplify this ratio by dividing both numerator and denominator by x^2.
So, the simplified ratio of the areas is 9:64.