Maths-

General

Easy

Question

# If the length of the diagonal of a square is 12 √2 cm, what is its perimeter?

Hint:

### Perimeter of a square = 4 ×side

All angles in a square are equal to 90°

Diagonal of a square divides it into 2 right angled triangles.

## The correct answer is: Perimeter of the given square is 48 cm.

### Step-by-step solution:-

In the adjacent diagram, we can see that the diagonal divides the given square into 2 right angled triangles.

Also, diagonal of the square becomes the hypotenuse of the 2 triangles.

Hypotenuse of the given triangles = diagonal of the given square = 12 √2 cm

Let the sides of the given square be x cm.

∴ side of the triangles (other than hypotenuse) = x cm.

By applying Pythagorean theorem, For a right angled triangle-

Hypotenuse2 = sum of the squares of the remaining 2 sides

∴ (12√2)2 = x2 + x2

∴ 144 × 2 = 2x2

∴ 288 = 2x2

i.e. 2x2 = 288

∴ x2 = 288 / 2

∴ x2 = 144

∴ x = 12 .............................. (Taking square root both the sides) ........................ (Equation i)

Perimeter of the given square = 4 × side

∴ Perimeter of the given square = 4 × x

∴ Perimeter of the given square = 4 × 12 ...................................................................................... (From Equation i)

∴ Perimeter of the given square = 48 cm

Final Answer:-

∴ Perimeter of the given square is 48 cm.

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