Question

Find the side and perimeter of a square whose diagonal is 10cm

Answer 1

refer the attachment

Answer 2

Refer the attachment for the figure.

Let AB = BC = x

AC = 10
Angle ABC = 90° ... angle of square

Using Pythagoras theorem,
AC^2 = AB^2 + BC^2
10^2 = x^2 + x^2
100 = 2x^2
50 = x^2
√50 = x
5√2 = x

So, Each side of square is 5√2 cm

Perimeter of square = 4 × side

= 4 × 5√2

= 20√2 cm

So, Side of square is 5√2 cm and Perimeter of square is 20√2.