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A rectangle has sides in the ratio 1 : 4. Consider a square with the same area as the rectangle, then what will be the ratio of the perimeter of the rectangle to square?
1. 4 : 5
2. 5 : 4
3. 3 : 2
4. 2 : 3

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Correct Answer - Option 2 : 5 : 4

Calculation:

Let a be the smaller side of rectangle,

4a is the length longer side.

Area of rectangle = Area of square

⇒ a × 4a = c2

⇒ c = 2a

Perimeter of rectangle = a + 4a + 4a + a =10a

Perimeter of square = 4 × 2a = 8a

Ratio is 10a : 8a = 5 : 4

∴ The ratio of their perimeter of rectangle to square is 5 : 4.

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