Question

the length of a diagonal of a square is 20 CM then its perimeter is

Answer 1

Hi ,

Let side of the square = a cm

Diagonal = d = 20 cm

a = d / √2

a = 20/√2 cm

Perimeter = 4a

P = 4 × ( 20/√2 )

= 80 √2 / 2

P = 40√2 cm

I hope this helps you.

:)

Answer 2

ANSWER WITH FULL EXPLANATION

Let the side of the square be $x$ cm.
Diagonal of the square = 20 cm
Now, using Pythagoras Theorem
$Side^{2}+Side^{2}=Diagonal^{2}$
=> $x^{2}+x^{2}=20^{2}$
=> $2x^{2}=400$
=> $\frac{2x^{2}}{2}=\frac{400}{2}$ [Dividing both sides by 2. ]
=> $x^{2}=200$
=> $\sqrt{x^{2}}=\sqrt{200}$ [Square root both sides. ]
=> $x=\sqrt{200}=\sqrt{2*2*2*5*5}=2*5*\sqrt{2}=10 \sqrt{2}$
=> $x=10 \sqrt{2}$

Now, we know that the measure of each side of the square is $10 \sqrt{2}$ cm.

Now,
Perimeter of the square
= 4 × Side
$=4*10 \sqrt{2}$
$=40 \sqrt{2}$ cm

So, the perimeter of the square is $40\sqrt{2}$ cm (56.56854... cm).

Hope this may help you.

If you have any doubt, then you can ask me in the comments.