How long is the side of a square picture that can fit inside a circular picture frame that has a diameter of 8 inches?
Hint: Pythagorean Theorem
a^2 + b^2 = c^2
a^2 + a ^2 = 8^2
2a^2 = 64
a^2 = 64/2
a^2 = 32
a = 5.6569
Find the circumference of a circle with a radius of 2.1cm.(Use 3.14 for pi.)
To determine the side length of the square picture, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the square picture will be the hypotenuse. The diagonal of a square divides it into two right triangles, each with a side length equal to half the length of the diagonal.
So, let's calculate the length of the diagonal of the square picture based on the diameter of the circular picture frame:
The diameter of the circular picture frame is given as 8 inches.
The radius, which is half of the diameter, is 8/2 = 4 inches.
The diagonal of the square picture would be equal to the diameter of the circular picture frame because the diagonal of a square is equal to the diameter of the circle that would fit inside it.
Therefore, the diagonal of the square picture is also 8 inches.
Now, we can use the Pythagorean Theorem to find the side length of the square picture:
Let's assume the side length of the square picture is "s" inches.
Using the Pythagorean Theorem:
s^2 + s^2 = diagonal^2
2s^2 = diagonal^2
2s^2 = 8^2
2s^2 = 64
s^2 = 64/2
s^2 = 32
Taking the square root of both sides to solve for "s", we get:
s = √32
Simplifying the square root, we have:
s ≈ 5.65 inches
Therefore, the side length of the square picture that can fit inside a circular picture frame with a diameter of 8 inches is approximately 5.65 inches.