Question

find the perimeter of a squar whose diagonal are 8 cm​

Answer 1

Diagonal of a square = a√2

Where a is one side of the square.

a√2 = 8

a = 8/√2

a = 4√2

One side= 4√2 cm

Perimeter= 4√2×4

= 16√2 cm

= 22.627417

~ 22.63cm.

HOPE THIS HELPS.

Answer 2

Appropriate question :

Find the perimeter of a square whose diagonal are 8cm.

Solution :

Let □ABCD be the given square.

l(diagonal AC) = 8cm, let the side of the square be x cm.

In ABC,

∠B = 90°

∴ AC² = AB² + BC² ( Pythagoras theorem)

∴ 8² = x² + x²

∴ 64 = 2x²

∴ x² = 64/2

∴ x² = 32

∴ x = √32 [ Taking square root of the both sides]

Perimeter of square = 4a

= 4 * √32

= 4 * √ 2*2*2*2*2

= 4*4√2

= 16√2

Hence the perimeter is 16√2.