Question

If the length of a diagonal of a square is 20cm, then it's perimeter is?

Answer 1

Heya !!!

This is your answer.

Given :-

Diagonal of square = 20 cm.

We know that Area of Square =
1/2 × d²

= 1/2 × 20 × 20
= 10×20
= 200 cm².

Also, area = side²
So,
side = √area
side = √200
Side = 10√2 cm.

Perimeter= 4 × side
= 4 × 10√2
= 40√2 cm.

Hence the perimeter of the square is 40√2 cm.

Hope it helps

Answer 2

Given,

Diagonal length of square = 20cm

To Find,

The perimeter of the square.

Solution,

Given that,

The square has a diagonal of 20cm.

The diagonal of the square,  d = side$\sqrt{2}$

Side =a.

d = a$\sqrt{2}$

20 = a$\sqrt{2}$

a = $\frac{20}{\sqrt{2} }$

a = $\frac{20}{\sqrt{2} }$×$\frac{\sqrt{2} }{\sqrt{2} }$

a = 10 $\sqrt{2}$cm.

Therefore,

the perimeter of the square 4a = 4×10$\sqrt{2}$

Perimeter = 40$\sqrt{2}$ cm.

Hence, 40$\sqrt{2}$cm is the perimeter of the square which has a diagonal of 20cm.