10. \( P=4 s \), when \( P=36 \mathrm{~cm} \)

To find the value of \( s \) when \( P = 36 \mathrm{~cm} \), you can use the formula \( P = 4s \). Plugging in the value for \( P \), you have: \[ 36 = 4s \] Now, solving for \( s \), divide both sides by 4: \[ s = \frac{36}{4} = 9 \mathrm{~cm} \] So, \( s = 9 \mathrm{~cm} \). If you were visualizing this, you could think of \( s \) as the length of one side of a square, and \( P \) as the perimeter. When you draw it out, it becomes clearer how the lengths relate! To further expand on shapes and their properties, it’s fascinating to note that in a square, all sides are equal. This simple geometry not only helps in understanding basic math principles but is also essential in fields like architecture, engineering, and even art. The aesthetic appeal of squares can be found in countless designs, from buildings to graphic layouts!