Question

Areas of two squares are in the ratio m² ∶ n⁴. What is the ratio of their perimeters?
1. m ∶ n
2. n ∶ m
3. m ∶ n²
4. m² ∶ n

Answer 1

Correct Answer - Option 3 : m ∶ n²

Given:

Ratio of area of two squares = m² ∶ n⁴

Formula used:

Area of square = (side)²

Perimeter of square = 4 × (side)

Calculation:

As we know that

Area of square = (side)²

Area of Square₁ = m² = (side₁)²

⇒ m = side₁

And, Area of Square₂ = n⁴ = (side₂)²

⇒ (n²)² = (side₂)²

⇒ n² = side₂

Now,

The ratio of Perimeters = Perimeter of Square₁ ∶ Perimeter of Square₂

⇒ (4 × side₁) ∶ (4 × side₂)

⇒ m ∶ n²

∴ The ratio of their perimeters is m ∶ n².