Question

the perimeter of a square is 40 c.m., find the length of its diagonal and its

Area.​

Answer 1

Answer:

Given:

There is a square given to us.

Perimeter of a square is 40cm.

To Find:

The length of diagonal of the square.

Answer:

Given , the perimeter of a square is 40cm.

Let each side be x

Perimeter =4 × side= 4 × x = 4x

4x = 40

x = 10cm

Area of square = side x side

                         = 4 x 4 = 16cm

In ∆ ABC ,

AC^2 = AB^2 +BC^2

         = 10^2 + 10^2

         = 100 + 100

         = 200

AC    = $\sqrt{200$

         = $\sqrt{10 X 10 X 2 }$

        =  10 $\sqrt{2}$ cm

Therefore the length of diagonal is 10√2cm.