square 1 has a side length of x, and square 2 has a side length of y. Square 2 is formed by joining the midpoints of the sides of square 1 in order. If x=2, find the ratio of the are of square 1 to the area of square 2
To find the ratio of the area of square 1 to the area of square 2, we first need to determine the side length of square 2.
Square 2 is formed by connecting the midpoints of the sides of square 1 in order. Since square 1 has a side length of x, the midpoints of each side will be at a distance of x/2 from each corner.
Therefore, square 2 will have a side length equal to the diagonal of square 1. We can find the diagonal using the Pythagorean theorem: diagonal^2 = (side length)^2 + (side length)^2.
Given that x = 2, the diagonal of square 1 is:
diagonal = sqrt(2^2 + 2^2) = sqrt(8) = 2 * sqrt(2).
Now that we have the side length of square 2, which is 2 * sqrt(2), we can find its area:
area of square 2 = (side length)^2 = (2 * sqrt(2))^2 = 4 * 2 = 8.
The area of square 1 is:
area of square 1 = (side length)^2 = 2^2 = 4.
Therefore, the ratio of the area of square 1 to the area of square 2 is:
ratio = area of square 1 / area of square 2 = 4 / 8 = 1/2.
Hence, the ratio of the area of square 1 to the area of square 2 is 1/2.
the value of x does not matter, if it is just the ratio of ares you want.
Just draw the figure, and it should be clear that (x/2)^2 + (x/2)^2 = y^2
simplify, and then your ratio is just x^2/y^2