Question

if the diagonal of a square is 12 √2 cm then the perimeter of a square is 48 . But How
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Answer 1

Answer:

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.

Answer 2

Given,

Diagonal of the square = $12\sqrt{2}$ cm

Perimeter of the square = 48 cm

To find,

Prove how the perimeter = 48 cm

Solution,

In a square all angles are in $90^{0}$

And, the relationship between diagonal and side of a square = $d = a\sqrt{2}$

So $a\sqrt{2} = 12\sqrt{2}$

Hence, a = 12 cm

In a square, all sides are equal.

Perimeter of the square = 4a = 4(12) = 48 cm

Therefore, perimeter of the square which as diagonal as $12\sqrt{2} cm$ is 48 cm