Question

The length of the diagonal of a square is 6 cm. Find the sides of the square.
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Answer 1

In a square, all sides are equal, and the diagonal divides the square into two 45-45-90 right triangles.

Let's denote the side of the square as "s" and the length of the diagonal as "d."

In a 45-45-90 triangle, the sides are in the ratio 1:1:√2. Therefore, the relationship between the side "s," the diagonal "d," and the hypotenuse of the triangle (which is also the diagonal) can be expressed as:

s : s : d = 1 : 1 : √2

Given that the length of the diagonal is 6 cm, we have:

s : s : 6 = 1 : 1 : √2

Now, solve for the side "s":

s = 6 / √2

To simplify the expression, rationalize the denominator:

s = (6 / √2) * (√2 / √2)

s = 6√2 / 2

s = 3√2 cm

Therefore, each side of the square is 3√2 cm.

Answer 2

The side of the square is 4.24 cm.

Explanation:

Given:

• The length of the diagonal of a square is 6 cm.

To find:

The sides of the square.

Solution:

In a square, all the sides are equal and the diagonals bisect each other at right angles.

Let the side of the square be x cm.

Since the diagonals bisect each other at right angles, we can apply the Pythagoras theorem to calculate the side of the square.

Pythagorean theorem:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the diagonal, which is 6 cm. The other two sides are AB = BC = x cm.

`\sf x^2 + x^2= 6^2`

`\sf 2x^2 = 36`

`\sf x^2= (36)/(2)`

`\sf x ^2 = 18`

`\sf x = √(18)`

`\sf x = 3√(2)`

`\sf x \approx 4.24 \textsf{ In 2.d.p}`

Therefore, the side of the square is 4.24 cm.