The corners of a square lie on a circle of diameter 0.4 m. Each side of the square has length L. Find L.
To find the length of each side of the square (L), we can use the fact that the corners of the square lie on a circle with a diameter of 0.4 m.
1. The diameter of a circle is twice the length of its radius. In this case, the diameter is given as 0.4 m. So, we can divide the diameter by 2 to find the radius.
radius = diameter / 2
= 0.4 m / 2
= 0.2 m
2. In a square, the diagonal is equal to the side length multiplied by the square root of 2 (Diagonal = L * √2). So, we can find the diagonal of the square using the radius we just calculated.
diagonal = 2 * radius
= 2 * 0.2 m
= 0.4 m
3. Since the corners of the square lie on the circle, the diagonal is equal to the diameter of the circle. Therefore, we equate the diagonal of the square to the diameter of the circle.
L * √2 = diagonal
L * √2 = 0.4 m
4. Now, we can solve for L by dividing both sides of the equation by the square root of 2.
L = 0.4 m / √2
5. We can simplify the value of L by rationalizing the denominator (i.e., multiplying both the numerator and denominator by √2).
L = (0.4 m / √2) * (√2 / √2)
= 0.4 m * √2 / 2
= (0.4√2) / 2
= 0.2√2 m
Therefore, the length of each side of the square (L) is approximately 0.2√2 m.