In the figure below, the area of the larger square is 50 square centimeters and the area of the smaller sqaure is 18 square centimeters. What is x, in centimeters?
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I can not see your figure.
To find the value of x, we need to first understand the relationship between the two squares. From the figure, we can see that the smaller square is inscribed inside the larger square. This means that the length of each side of the smaller square is equal to the distance between the outer corner of the smaller square and the corresponding corner of the larger square.
Let's denote the length of the smaller square's side as s, and the length of the larger square's side as S.
We are given that the area of the larger square is 50 square centimeters, so we can write the equation:
S^2 = 50
Similarly, the area of the smaller square is 18 square centimeters, so we can write the equation:
s^2 = 18
To find the value of x, we need to find the difference between the lengths of the sides of the two squares. Since we know that the side length of the smaller square is equal to the distance between the outer corner of the smaller square and the corresponding corner of the larger square, we can express this difference as:
x = S - s
To solve for x, we need to solve the system of equations composed of S^2 = 50 and s^2 = 18. By solving these equations simultaneously, we can find the values of S and s. Then, we can substitute these values into the equation x = S - s to find the value of x.
To find the length of the side of the smaller square, we can take the square root of its area.
Area of the smaller square = 18 square centimeters
So, the length of the side of the smaller square = √18 cm
To find the length of the side of the larger square, we can use the proportion of their areas.
Area of the larger square = 50 square centimeters
Area of the smaller square = 18 square centimeters
So, (side of the larger square)^2 / (side of the smaller square)^2 = 50 / 18
(side of the larger square)^2 / (√18 cm)^2 = 50 / 18
(side of the larger square)^2 = (50 / 18) * (√18 cm)^2
(side of the larger square)^2 = (50 / 18) * 18 cm
(side of the larger square)^2 = 50 cm
Taking the square root of both sides, we get:
side of the larger square = √50 cm
Since the larger square consists of the smaller square and two equal triangles, we can write:
(side of the larger square) = (side of the smaller square) + 2(x)
√50 cm = √18 cm + 2x cm
Now, we can solve for x by rearranging the equation:
√50 cm - √18 cm = 2x cm
x = (√50 cm - √18 cm) / 2
Therefore, x is equal to (√50 cm - √18 cm) / 2 cm.