the perimeter of a square is 56. express, the lenght of a diagonalof the square in simplest radical form.

if the perimeter is 56, isn't each side equal to 14 ?

then using Pythagoras,
if we call the diagonal x,
x^2 = 14^2 + 14^2 = 392
x=√392 = 14√2

Why did the square go to the doctor?

Because it was feeling a little "obtuse"!

But, let's get back to your question. Remember that in a square, all sides are equal in length. So, if the perimeter is 56, we can divide it by 4 to find the length of each side.

56 / 4 = 14

Now, let's find the length of the diagonal. In a square, the diagonal is the hypotenuse of an isosceles right triangle.

Using the Pythagorean theorem, we can find the length of the diagonal.

Let's call the length of the diagonal 'd', and the length of one side 's'.

d² = s² + s²

d² = 2s²

d = √(2s²)

Substituting the value of 's' we found earlier:

d = √(2 * 14²)

d = √(2 * 196)

d = √(392)

d = √(4 * 98)

d = 2√98

So, the length of the diagonal in simplest radical form is 2√98.

To find the length of the diagonal of a square, we first need to find the length of one side. Since the perimeter of the square is given as 56, we can divide it by 4 (as a square has four equal sides) to find the length of one side.

Perimeter of a square = 4 * side length

56 = 4 * side length

Divide both sides by 4:

side length = 56 / 4 = 14

Now that we know the side length is 14, we can use the Pythagorean theorem to find the length of the diagonal (d) of the square:

d² = side length² + side length²

d² = 14² + 14²

d² = 196 + 196

d² = 392

Taking the square root of both sides, we get:

d = √392

Finally, we simplify the radical (if possible):

d = √(4 * 98) = √(4 * 49 * 2) = √(2 * 2 * 7 * 7 * 2) = 14√2

Therefore, the length of the diagonal of the square is 14√2.

To find the length of the diagonal of a square, we can use the Pythagorean theorem. In a square, the diagonal and the sides form a right triangle.

Let's denote the length of each side of the square as "s" and the length of the diagonal as "d". We know that the perimeter of the square is 56, so the sum of all four sides is 56.

Since all four sides are equal in a square, we can express the perimeter as 4s:

4s = 56

Now, let's solve for "s" by dividing both sides of the equation by 4:

s = 56/4
s = 14

So, each side of the square has a length of 14 units.

Now, using the Pythagorean theorem, we can find the length of the diagonal:

d^2 = s^2 + s^2 (since we have a right triangle formed by the diagonal and two sides)
d^2 = 14^2 + 14^2
d^2 = 196 + 196
d^2 = 392

To express the length of the diagonal in simplest radical form, we find the square root of 392:

d = √392

Now, we simplify the square root. The prime factorization of 392 is 2^3 * 7^2. Since we need to simplify, we take out pairs of identical factors from under the square root:

d = √(2^2 * 2 * 7^2)
d = √(2^2) * √(2 * 7^2)
d = 2 * 7 * √2
d = 14√2

Therefore, the length of the diagonal of the square is 14√2 units in simplest radical form.