Question

the diagonal of a square is 20√2 cm. find its perimeter​

Answer 1

ANSWER:

Perimeter of square=80cm

EXPLAINATION:

Here in this question concept of Pythagoras theorem as well as perimeter of square is used. As we know that diagonals of a square forms an isosceles right angled triangle with the sides of square as shown in the attachment. So we can find the sides of square by using Pythagoras theorem. By substituting value of side in formula of perimeter of square, we can find its perimeter.

$\rule{250}{2}$

So let's start!

Let us assume each side of square be x.

In ∆ ABC, AC is diagonal.

Applying Pythagoras theorem:

AC²=AB²+BC²

(20√2cm)²=x²+x²

800cm²=2x²

Divide 2 from both LHS and RHS.

400cm²=x²

√400cm²=x

√20cm×20cm=x

20cm=x

So each side of square is 20cm.

$\rule{250}{2}$

Now applying formula of perimeter:

★ Perimeter of square=4×Side

Perimeter of square=4×20cm

Perimeter of square=80cm

Hence the required perimeter is 80cm.

Answer 2

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.