Questions: 7. Find the exact length of one side of a square with a diagonal that measures 16 centimeters.

Solution Steps

To find the length of one side of a square given its diagonal, we can use the Pythagorean theorem. In a square, the diagonal forms a right triangle with two sides of the square. If \( s \) is the side length and \( d \) is the diagonal, then \( d = s\sqrt{2} \). Solving for \( s \), we get \( s = \frac{d}{\sqrt{2}} \).

In a square, the diagonal forms a right triangle with two sides of the square. Using the Pythagorean theorem, we know that for a square with side length \( s \) and diagonal \( d \):

\[ d = s\sqrt{2} \]

To find the side length \( s \), we rearrange the equation:

\[ s = \frac{d}{\sqrt{2}} \]

Given that the diagonal \( d \) is 16 cm, we substitute this value into the equation:

\[ s = \frac{16}{\sqrt{2}} \]

Simplifying the expression, we get:

\[ s = \frac{16}{1.4142} \approx 11.3137 \]

Final Answer