find the perimeter of a square with a diagonal of 6 square root 2 in.

Question

Generate an appealing, mathematical image of a square due to a geometry problem. The square has a diagonal clearly marked with the numerical value of '6 √2'. There should be no text present within the image. To provide context, depict a ruler next to the square for scale and a pencil with an eraser at one end, indicating that the geometry problem is in the process of being solved. The background should be a typical graph paper to give it an authentic mathematical problem-solving context.

find the perimeter of a square with a diagonal of 6 square root 2 in.

I am not sure how to figure out this perimeter.

Answer 1

You are told it is a square so the sides are of equal length, a.

If we wanted to find the length of the diagonal of a square with sides length a, then

diagonal = sqrt(2a^2)
=6sqrt(2)

sqrt(2a^2)= 6sqrt(2)
2a^2 = 36 x 2

a^2 = 36

so a=6

now find the perimeter

Answer 2

To find the perimeter of a square with a diagonal, you can use the Pythagorean theorem.

In a square, all sides are of equal length, so let's call the length of one side "s".

The diagonal of the square forms a right triangle with two sides of length "s". The diagonal is given as 6√2 inches.

Applying the Pythagorean theorem, we have:

s^2 + s^2 = (6√2)^2
2s^2 = 36*2
2s^2 = 72

Dividing by 2, we get:

s^2 = 36

Taking the square root of both sides:

s = √36

s = 6 inches

Therefore, each side of the square is 6 inches long.

The perimeter of a square is calculated by multiplying the length of one side by 4:

Perimeter = 6 inches * 4 = 24 inches

So, the perimeter of the square is 24 inches.

Answer 3

To find the perimeter of a square, you need to know the length of one side. However, in this case, you are given the length of the diagonal. We can use the relationship between the diagonal and the side length of a square to find the perimeter.

The diagonal of a square creates a right triangle with the sides of the square. Let's call the side length of the square "s" and the diagonal "d". In this case, the diagonal is given as 6√2 inches.

In a right triangle, the hypotenuse (which is the diagonal) is equal to the square root of the sum of the squares of the other two sides. Using this, we can write the equation as:

d = √(s^2 + s^2)

Substituting the given diagonal:

6√2 = √(s^2 + s^2)

Squaring both sides of the equation:

(6√2)^2 = (s^2 + s^2)^2
72 = 2s^2

Dividing both sides by 2:

36 = s^2

Taking the square root of both sides:

s = √36 = 6

Now that we have the length of one side of the square as 6, we can find the perimeter by multiplying the side length by 4 (as a square has four equal sides):

Perimeter = 4 * s
Perimeter = 4 * 6
Perimeter = 24 inches

Therefore, the perimeter of the square with a diagonal of 6√2 inches is 24 inches.