The perimeter of a square is 64 cm. The area of a rectangle is 16 cm2 less than the area of the square. If the length of rectangle is 20 cm, what is the perimeter of the rectangle?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 64 cm.
Given:
The perimeter of a square is 64 cm.
The area of a rectangle is 16 cm2 less than the area of the square.
The length of rectangle is 20 cm
Formula used:
Perimeter of the square = 4a
Area of square = a2
Area of rectangle = l × b
Perimeter of rectangle = 2(l + b)
where, a = side of square, l = length of rectangle and b = breadth
Calculations:
Using equation (1), we get
Perimeter of square = 4a
⇒ 4a = 64
⇒ a = 16
Using equation (2),
Area of square = a2
⇒ 162 = 256
According to the question;
Area of rectangle = Area of square - 16
⇒ Area of rectangle = 256 - 16 = 240
⇒ 20 × b = 240
⇒ b = 12
Perimeter of the rectangle = 2(l + b)
⇒ 2(20 + 12) = 2(32) = 64 cm