square x has an area of 100 square units. Square Y has a perimeter that is half of the perimeter of square x. What is the area of square y?
each side of x is 10 units since it is square
then each side of y must be 5 units
and its area is 25 square units
In fact the ratio of areas of any two similar figures is the square of the linear scale ratio between them.
Square X, s = side
Area, A = s^2
100 = s^2
Take square root of both sides
10 = s
Square X, s = side
Perimeter, P = 4s
s = 10
P = 4(10)
P = 40
Square Y, s = side
Perimeter of Sq. Y = 1/2 Sq. X
Perimeter of Sq X = 40,
P = 1/2 (40) = 20
P = 4s
20 = 4s
s = 5
Square Y, side = s
Area, A = s^2
s = 5
A = 5^2
A = 25 sq units
To find the area of square Y, let's first calculate the perimeter of square X.
The area of square X is given as 100 square units. The formula to calculate the area of a square is side x side, where "side" represents the length of one side of the square.
So, the formula for the area of square X is s x s = 100, where "s" represents the side length of square X.
To find the side length of square X, we can take the square root of 100:
√100 = 10
Therefore, the side length of square X is 10.
The perimeter of square X is the sum of all four sides of the square, which are all equal. Since the perimeter of square Y is half of the perimeter of square X, we can find the perimeter of square Y.
Perimeter of square X = 4 x side length of square X = 4 x 10 = 40
Perimeter of square Y = 1/2 x perimeter of square X = 1/2 x 40 = 20
Now, let's determine the side length of square Y. Since the perimeter of square Y is half of the perimeter of square X, the lengths of all four sides of square Y are also half of the side length of square X.
Side length of square Y = side length of square X / 2 = 10 / 2 = 5
Finally, to find the area of square Y, we square the side length:
Area of square Y = side length x side length = 5 x 5 = 25 square units
Therefore, the area of square Y is 25 square units.
To find the area of square Y, we need to determine its side length first. Let's break it down step by step:
1. Given that square X has an area of 100 square units, we can calculate its side length. The formula for the area of a square is side length squared, so in this case, we have:
Area of Square X = Side length of Square X x Side length of Square X
100 = Side length of Square X x Side length of Square X
Solving this equation, we find that the side length of Square X is √100 = 10 units.
2. Next, we are told that Square Y has a perimeter that is half of the perimeter of Square X. The perimeter of a square is four times its side length, so for Square Y:
Perimeter of Square Y = 4 x Side length of Square Y
Perimeter of Square X = 4 x Side length of Square X
Since the perimeter of Square Y is half of Square X, we can write the equation:
4 x Side length of Square Y = 1/2 x (4 x Side length of Square X)
4 x Side length of Square Y = 1/2 x (4 x 10)
4 x Side length of Square Y = 1/2 x 40
4 x Side length of Square Y = 20
Solving this equation, we find that the side length of Square Y is 5 units.
3. Finally, we can calculate the area of Square Y using its side length:
Area of Square Y = Side length of Square Y x Side length of Square Y
Area of Square Y = 5 x 5
Area of Square Y = 25 square units
Therefore, the area of Square Y is 25 square units.