Question

the diagonal of a square is 20 cm find the side of the square and perimeter​

Answer 1

the diagonal of the square and the two equal sides form a right angle triangle at 90 degree .

let the similar side of the square be a.

then by Pythagoras theorem ,

20² = a² + a²

20² = 2a²

400 = 2a²

200 = a²

a = √200 = √2*100 = 10√2

now, perimeter = 4* 10√2 = 56.56 cm

area = 10√2*10√2 = 100*2 = 200cm²