The diagonal of a square is 10√2 cm, find its perimeter?

Question

Question

Answer 1

As seen from the above figure,

The diagonal AC = 10√2

Now ABC forms a right angled triangle with AB = BC

By Pythagoras theorem,

AB² + BC² = AC²

2AB²= 100 × 2

AB² = 100

AB = 10

Perimeter of a square = 4 AB = 40 cm

ALTERNATE SOLUTION:

For any square of side "a"

Diagonal = a√2

Hence, a√2 = 10√2

⇒ side = a = 10

Perimeter of a square = 4a

∴ Perimeter of a square = 40 cm