the length of a diagonal of a square is 22 square root of 2 millimeters. Find the perimeter of the square.

Question

the length of a diagonal of a square is 22 square root of 2 millimeters. Find the perimeter of the square.

Answer 1

To find the perimeter of a square, we need to know the length of one side. We can use the length of the diagonal to find the length of one side of the square.

Let's assume 's' is the length of one side of the square.

Using the Pythagorean theorem, we know that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

In this case, the diagonal of the square (c) is equal to 22√2 mm. Let's set up the equation.

c^2 = a^2 + b^2

(22√2)^2 = s^2 + s^2

484 * 2 = 2s^2

968 = 2s^2

Now, let's simplify the equation to solve for 's'.

484 = s^2

Taking the square root on both sides, we get:

s = √484

s = 22 mm

Now that we know the length of one side of the square is 22 mm, we can find the perimeter.

Perimeter of a square = 4 * s

Perimeter = 4 * 22

Perimeter = 88 mm

Therefore, the perimeter of the square is 88 millimeters.

Answer 2

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

In a square, the diagonal forms a right triangle with two sides that are equal in length (the sides of the square). Let's call the length of one side of the square "s".

According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse. In this case, the hypotenuse is the diagonal.

So, we can set up the equation:
s^2 + s^2 = (22√2)^2
2s^2 = 22^2 * 2
2s^2 = 484 * 2
2s^2 = 968

Dividing both sides of the equation by 2, we get:
s^2 = 484

Taking the square root of both sides, we get:
s = √484
s = 22

Therefore, the length of one side of the square is 22 millimeters.

Now that we know the length of one side, we can find the perimeter of the square by multiplying the length of one side by 4 (as a square has four equal sides).
Perimeter = 4 * s
Perimeter = 4 * 22
Perimeter = 88

Hence, the perimeter of the square is 88 millimeters.

Answer 3

The diagonal forms a right triangle with 2 sides of the square. The sides are of equal length, so you can use Pythagorean Theorem to find a side of the square.

the length of a diagonal of a square is 22 square root of 2 millimeters. Find the perimeter of the square.

To find the perimeter of a square, we need to know the length of one side. We can use the length of the diagonal to find the length of one side of the square.

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

thanks!

The diagonal forms a right triangle with 2 sides of the square. The sides are of equal length, so you can use Pythagorean Theorem to find a side of the square.