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**Hint:**As we know the side of the given square is \[10cm\]. And in a square, all the four sides are equal to each other as well as all the sides interest to its adjacent side at \[{90^0}\]. Therefore, the figure formed by joining the two opposite vertices of a square, is a right-angled triangle with two equal sides.

**Complete step-by- step solution:**

Given that Side of the square is \[10cm\]

In right angled\[\vartriangle ABC\]

Using Pythagoras theorem

\[A{B^2} + B{C^2} = A{C^2}\] \[\left[ {Bas{e^2} + Perpendicular{r^2} = Hypotenuse{e^2}} \right]\]

As we know, the sides of a square are equal to each other.

$\Rightarrow$ \[AB = BC\]

$\Rightarrow$\[{10^2} + {10^2} = A{C^2}\]

$\Rightarrow$\[100 + 100 = A{C^2}\]

$\Rightarrow$\[200 = A{C^2}\]

$\Rightarrow$\[AC = \sqrt {200} \]

$\Rightarrow$\[AC = \sqrt {2 \times 2 \times 2 \times 5 \times 5} \]

$\Rightarrow$\[AC = 2 \times 5\sqrt 2 \]

$\Rightarrow$\[AC = 10\sqrt 2 \]

Therefore, the diagonal of square will be \[10\sqrt 2 \]

**Note:**A square can have two diagonals. Each of the diagonal can be formed by joining the diagonally opposite vertices of a square. The properties of diagonals are as follows-

Both the diagonals are congruent (same length). Both the diagonals bisect each other, i.e. the point of joining of the two diagonals is the midpoint of both the diagonals. A diagonal divides a square into two isosceles right-angled triangles. The sum of all the internal angles of a square is equal to \[360 \circ \]and a square is a regular quadrilateral that has four equal sides and four same angles.

The diagonal of a square with side ‘a’ can be calculated using a formula \[a\sqrt 2 \]. Remember, both the diagonals of a square are equal to each other.

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