The corners of a square lie on a circle of diameter 0.33 m. Each side of the square has length L. Find L.
The diameter of the circle is the hypotenuse of the two triangles formed in the square.
Use the Pythagorean theorem to find out the length of the sides.
How would i determine that with only one value?
Each side of the square is the same length.
Im still confused. Wouldnt each side just be 0.33 m then?
0.33 is the hypotenuse
See this rough sketch.
http://www.scriblink.com/index.jsp?act=phome&ld=1&rid=600&cid=750
To find the length of each side of the square, let's go step by step:
1. Start with the information given: The corners of the square lie on a circle of diameter 0.33 m.
2. Recall that a square has equal sides, so all sides of the square are the same length.
3. Consider that the diagonal of a square is equal to the diameter of the circumscribed circle. In other words, the diagonal of the square is equal to the diameter of the circle in which it is inscribed.
4. The diagonal of the square is the hypotenuse of a right triangle formed by two adjacent sides of the square.
5. Use the Pythagorean theorem to find the length of the diagonal (D) of the square. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, it becomes:
D^2 = L^2 + L^2
= 2L^2
where L represents the length of each side of the square.
6. With the diagonal length (D) being the diameter of the circle, D = 0.33 m.
7. Substitute D = 0.33 m into the equation from step 5:
0.33^2 = 2L^2
Simplifying,
0.1089 = 2L^2
8. Divide both sides of the equation by 2:
0.05445 = L^2
9. Take the square root of both sides to find L:
√0.05445 = L
L ≈ 0.2337 m
Therefore, the length of each side of the square is approximately 0.2337 meters.