The area of a square and rectangle are equal. The length of the rectangle is greater than the length of a side of the square by 10 cm and the breadth is less than 5 cm. The perimeter(in cm)of the rectangle is:

50

We know that,

Area of rectangle = Length × Breadth

Area of square = (Side)²

Perimeter of rectangle = 2(Length + Breadth)

We have,

Length = (Side of square + 10 cm)

Breadth = (Side of square – 5 cm)

Consider the length of side of square = s

Let Length and Breadth of a rectangle be l & b respectively

s² = (l × b)

= s² = [(s + 10) × (s - 5)]

= s² = s² – 5s + 10s – 50

= 5s = 50

= s = 10

l = (s + 10) = 20

b = (s - 5) = 5

Perimeter of Rectangle = 2(20 + 5) = 50