Question

If the side of a square is 4 cm. Find the length of the diagonal​

Answer 1

Given: The side of the square$=4cm.$

We have to find the length of the diagonal​ of the square.

For this, we are using the Pythagorean theorem.

As we know that the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

And as we know that all sides of the square are equal and the diagonal is equal to hypoteuse.

$\therefore$ All sides of the square will be$4cm.$

Let assume the length of the diagonal will be $x.$

$=>4^{2}+4^{2} =x^{2}\\=>16+16=x^{2} \\=>32=x^{2} \\=>\sqrt{32} =x\\=>x=5.656\\=>x=6$

Hence, the length of the diagonal​ will be $6cm.$

Answer 2

To find : length of diagonal

Given: side of the square = $4 \ cm$.

Solution:

• As wee know that all sides of square are equal.
• And also each side of square  makes a right angle with the adjacent side. i.e. ∠ 90° .
• Therefore, let ABCD be a square with side $4 \ cm$.
• And let , $AB = BC= CD =DA = 4\ cm$
• Let, vertex $B$ make right angle .

• Therefore applying  Pythagoras theorem in Δ ABC,

             $\begin{array}{l}A B^{2}+B C^{2}=A C^{2} \\4^{2}+4^{2}=A C^{2} \\2 \times 4^{2}=A C^{2}\\ A C=4 \sqrt{2} \mathrm{~cm}\end{array}$

   Hence , length of diagonal $AC$ is $4\sqrt{2}$ .