Maths-

General

Easy

Question

# If the sum of the lengths of the diagonals is 144cm. What will be the perimeter of a square ?

Hint:

### Perimeter of a square = 2 √2 d

Diagonals of a square are equal in measure.

## The correct answer is: ∴ Perimeter of the given square is 144 √2 cm.

### Step-by-step solution:-

For a square, Lengths of the diagonals are equal

Let D1 & D2 be the 2 diagonals

∴ D1 + D2 = 144 …........................................................... (As per given information)

∴ D1 + D1 = 144 ….......................................................... (Diagonals of a square are equal)

∴ 2 D1 = 144

∴ D1 = 144 / 2

∴ D1 = 72 cm.

i.e. D1 = D2 = 72 cm ...................................................... (Equation i)

Perimeter of a square = 2 √2 d

∴ Perimeter of a square = 2 √2 × 72 ................................ (From Equation i)

∴ Perimeter of a square = 144 √2 cm.

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