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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

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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.

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