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:
Answer & explanation
Correct answer: option 1
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