Question

If the length of a diagonal of a square is 20 cm, find: a. side of the square b. perimeter of the square​

Answer 1

From the given question the correct answer is:

the side of the square is $10\sqrt{2}$cm.

the perimeter of the square is $40\sqrt{2}$cm.

Given :

a diagonal of a square is 20 cm

To find:

a. side of the square

b. the perimeter of the square​

Solution:

we have to find the side of the square

Let, side of the square be x.

so we will use the Pythagoras theorem.

$x^{2} +x^{2} = 20^{2} cm$

$2x^{2} =400cm$

$x^{2} = 200$

$x=\sqrt{200}$

$x=10\sqrt{2}cm$

so, the side of the square is $10\sqrt{2}$cm.

now, we have to find the perimeter of the square.

the perimeter of the square = 4×side

                                        =4×$10\sqrt{2}$cm.

                                         =$40\sqrt{2}$cm

hence, the perimeter of the square is $40\sqrt{2}$cm.

   

Answer 2

Step-by-step explanation:

Solution :

In □ ABCD and ∆ ABC,

• Diagonal = 20 cm
• Base = BC
• Height = AB

As it is a square, the height and base will be the measures of the square's side.

(Refer the attachment)

★ a. side of the square :

Let,

Side of square = x

According to the Pythagoras Theorem,

⇒ (Hypotenuse)² = (Base)² + (Height)²

⇒ (AC)² = (BC)² + (AB)²

⇒ (20)² = (x)² + (x)²

⇒ 400 = 2x²

⇒ x² = 400/2

⇒ x² = 200

⇒ x = √200

⇒ x = 10√2

Side of square = 10√2 cm

___________________

★ b. perimeter of the square :

Perimeter of the square = 4 × side

⇒ 4 × 10√2

⇒ 40√2

Perimeter of the square = 40√2 cm

Therefore,

a. Side of square = 10√2 cm

b. Perimeter of the square = 40√2 cm