A square has diaonal of 24cm what is the lenght of its sides?. pls help me quick homework due tommorow

If a square is divided into two triangles by its diagonal, it will form 2 special right triangles. These right triangles will have the angle measures 45 degrees, 45 degrees, and 90 degrees. The diagonal of the square will be the hypotenuse for each of these isosceles right triangles and the side lengths of the square will be the legs.

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Through Pythagoras' Theorem

To find the length of the sides of a square when given the length of its diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's denote the length of the sides of the square as ( s ) and the length of the diagonal as ( d ).

According to the Pythagorean theorem:

[ d^2 = s^2 + s^2 ]

Given that the length of the diagonal (( d )) is 24 cm, we can substitute this value into the equation:

[ 24^2 = s^2 + s^2 ]

[ 576 = 2s^2 ]

Now, divide both sides by 2:

[ s^2 = \frac{576}{2} ]

[ s^2 = 288 ]

Now, take the square root of both sides to solve for ( s ):

[ s = \sqrt{288} ]

[ s = \sqrt{144 \times 2} ]

[ s = 12\sqrt{2} ]

Therefore, the length of each side of the square is ( 12\sqrt{2} ) cm.