The areas of two adjacent squares are 256 square inches and 16 square inches, respectively, and their bases lie on the same line. What is the number of inches in the length of the segment that joins the centers of the two inscribed circles? Express your answer as a decimal to the nearest tenth.
anon why would you say the answer without how??? how am i suppose to do my math test now :(((
X1^2 = 256,
X1 = 16 in. = lenth of each side = dia.
of circle.
X2^2 = 16,
X2 = 4 in. = length of each side = dia.
of circle.
L = r1 + r2 = 16/2 + 4/2 = 10 i. = length of segment.
Henry, you are wrong
The correct answer is 11.7
how do you get 11.7
To find the length of the segment that joins the centers of the two inscribed circles, we first need to determine the side lengths of the two squares.
Let's call the side length of the larger square "a" and the side length of the smaller square "b".
The area of a square is equal to the side length squared. So we have:
a^2 = 256 (Equation 1)
b^2 = 16 (Equation 2)
To find the side lengths, we take the square root of both sides of each equation:
a = √256 = 16 (since 16^2 = 256)
b = √16 = 4 (since 4^2 = 16)
Now that we have the side lengths, we can find the length of the segment that joins the centers of the two inscribed circles.
The centers of the circles will be located at the midpoints of the diagonals of each square. Since the diagonals of a square are equal in length, the length of the segment joining the centers of the circles will be equal to the difference in the side lengths of the two squares.
Let's calculate:
Length of the segment joining the centers = a - b = 16 - 4 = 12 inches.
Therefore, the length of the segment that joins the centers of the two inscribed circles is 12 inches.