A rectangle with perimeter 50 cm has its sides in the ratio 1 : 4. What is the perimeter of a square whose area is the same as that of the rectangle?

40 cm

We know that,

Perimeter of rectangle = 2(l + b)

Area of a rectangle = l × b

Area of a square = a²

Given,

Perimeter of square = 4a

Perimeter = 50 cm

Ratio of sides = 1 ∶ 4

Let sides of the rectangle a and 4a

= 2(a + 4a) = 50

= 5a = 25

= a = 5

So, area of the rectangle = 4a² = 4 × 25 = 100

a² = 100

a = 10

Perimeter = 4 × 10 = 40 cm