If the diagonal of a square is √48 what is the area of a square​

Step-by-step explanation:

Required perimeter of this square is 48 cm.

Step-by-step explanation:

If length of a diagonal of a square is 12√2 cm.

Let the length of each of that square be a cm. From the properties of square we know that the sides( adjacent ) of square intersect each other at 90°.

Thus, by Pythagoras theorem : -

= > side^2 + side^2 = diagonal^2

= > ( a cm )^2 + ( a cm )^2 = ( 12√2 cm )^2             [ since length of diagonal is 12√2 cm ]

= > a^2 cm^2 + a^2 cm^2 = 144 x 2 cm^2

= > 2a^2 cm^2 = 144 x 2 x cm^2

= > a^2 = 144

= > a^2 = 12^2

= > a = 12

Hence the required length of each side of square is 12 cm.

From the properties of square : -

Perimeter of square = 4 x square

Therefore,

= > Perimeter of this square = 4 x 12 cm

= > Perimeter of this square = 48 cm

Hence the required perimeter of this square is 48 cm