Question

Find the side and perimeter of square whose diagonal is 10cm ​

Answer 1

Let’s the measures of the sides of the square be x for now.
We know that the diagonal and 2 sides are creating an right angles triangle, in which the diagonal is the hypotenuse and the sides are the legs.
Now we can use the Pythagorean criteria:
x^2 +x^2 = 10^2cm
x^4=100cm

Answer 2

Sides :

Let's name the four corners of square ABCD.

AB= BC=CD=DA

We can slove this question by Pythagoras theorem

Let side be a cm.

$AB {}^{2} + AD {}^{2} = BD {}^{2} \\ a { }^{2} + a {}^{2} = BD {}^{2} \\ 2a {}^{2} = 10 {}^{2} \\ a {}^{2} = \frac{100}{2} \\ a = \sqrt{50} \\ a = 5 \sqrt{2}$

So, the sides of square is 5√2 cm.

Perimeter:

$perimeter \: of \: square \: = 4 \times side \\ = 4 \times 5 \sqrt{2} \\ = 20 \sqrt{2}$

So, the perimeter of square is 20√2 cm.