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