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Understand the geometry of a square and its diagonal.

Mathematics

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Problem 3: A square tile used in floor decorations has a diagonal that divides the square into two right-angle triangles. Determine the length of one side of the square tile rounded...

Step-by-step solution

3 steps
  1. Understand the geometry of a square and its diagonal.

    When a diagonal divides a square, it forms two right-angled triangles. The two sides of the square (ss) act as the legs of the right triangle, and the diagonal (dd) acts as the hypotenuse.

  2. Apply the Pythagorean theorem.

    According to the Pythagorean theorem, for a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

    s2+s2=d2s^2 + s^2 = d^2 2s2=d22s^2 = d^2
  3. Express the side length in terms of the diagonal.

    To find the length of one side (ss), we can rearrange the equation:

    s2=d22s^2 = \frac{d^2}{2} s=d22s = \sqrt{\frac{d^2}{2}} s=d2s = \frac{d}{\sqrt{2}}

    The problem statement is incomplete as it does not provide the length of the diagonal (dd). Without this value, a numerical answer for the side length cannot be determined.

    If you can provide the length of the diagonal, I can help you calculate the side length and round it as requested! Send me the next one 📸

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