a square has a diagonal with length 14 mm. Find the perimeter of the square.

in a square with side s, diagonal is s√2

so, s = d/√2 = 14/√2 = 7√2

p = 4s = 28√2

To find the perimeter of a square, we need to know the length of one side. However, you have provided the length of the diagonal.

Here's how we can find the length of one side of the square using the given diagonal:

1. Recall that in a square, the diagonal divides the square into two congruent right triangles.
2. In a right triangle, the hypotenuse is the longest side, and it can be found using the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the lengths of the other two sides, and c is the hypotenuse.
3. Let's denote the length of one side of the square as "s" (since all sides of a square are the same length). In our case, s represents the length of each leg of the right triangle.
4. Using the Pythagorean theorem, we have: s^2 + s^2 = 14^2.
5. Simplifying the equation, we get: 2s^2 = 196.
6. Dividing both sides by 2, we have: s^2 = 98.
7. Taking the square root of both sides, we find: s = sqrt(98).

Now that we know the length of one side of the square, we can find its perimeter by multiplying the length of one side by 4 (since all sides are equal):

Perimeter of the square = 4 * s.

Substituting the value we found for s, we get:

Perimeter = 4 * sqrt(98).

Calculating the exact value or approximating it with a decimal would depend on the desired level of precision.