The area of a rectangle is 48 cm² more than that of a square. If the length of the rectangle is 4 cm more than the side of the square and the breadth of the rectangle is 2 cm less than the side of the square, then find the perimeter of both the square and the rectangle.
Show answer & explanation
Correct answer: B
Explanation
Given:
Area of the rectangle = 48 cm² more than the area of the square
Length of the rectangle = 4 cm more than the side of the square
Breadth of the rectangle = 2 cm less than the side of the square
By the formula:
Area of the square = a²
Area of the rectangle = l × b
Let the side of the square = x
Length of the rectangle = x + 4
Breadth of the rectangle = x − 2
As per the question:
(x + 4)(x − 2) = x² + 48
x² + 2x − 8 = x² + 48
2x = 56
x = 28
Perimeter of the square = 4 × 28 = 112 cm
Length of the rectangle = 28 + 4 = 32
Breadth of the rectangle = 28 − 2 = 26
Perimeter of the rectangle = 2(32 + 26) = 116 cm
Perimeter of the square = 112 cm
Perimeter of the rectangle = 116 cm