The word pair "Circle : Circumference" implies a specific relationship between the two words. A circle is a geometric shape, and the circumference is a measurement associated with that shape. In other words, the circumference is a property or characteristic of a circle. To find the circumference of a circle, one needs to know the radius or diameter of the circle.

Let's analyze the given options and determine which one exhibits a similar relationship:

a) Triangle: Area - A triangle is a geometric shape, and the area is a measurement associated with that shape. However, the relationship between a triangle and its area is different from the relationship between a circle and its circumference. The area of a triangle is determined by its base and height, whereas the circumference of a circle is determined by its radius or diameter. Therefore, option A is not the correct answer.

b) Plane: Dimension - A plane is a two-dimensional surface, and dimension refers to the measurement of length, width, or height. While both words are related to measurement, the relationship between a plane and its dimension is different from the relationship between a circle and its circumference. Therefore, option B is not the correct answer.

c) Square: Diagonal - A square is a geometric shape, and the diagonal is a measurement associated with that shape. However, the relationship between a square and its diagonal is different from the relationship between a circle and its circumference. The diagonal of a square is determined by its side length, whereas the circumference of a circle is determined by its radius or diameter. Therefore, option C is not the correct answer.

d) Rectangle: Perimeter - A rectangle is a geometric shape, and the perimeter is a measurement associated with that shape. The relationship between a rectangle and its perimeter is similar to the relationship between a circle and its circumference. The perimeter of a rectangle is determined by adding the lengths of all its sides, whereas the circumference of a circle is determined by multiplying the diameter by pi (π) or by multiplying the radius by 2π. Both the perimeter and circumference represent the total length around the shape. Therefore, option D is the correct answer.

In conclusion, the word pair "Rectangle : Perimeter" exhibits the same relationship as the word pair "Circle : Circumference." Both pairs involve a geometric shape and a measurement associated with that shape.

Relation between Circle and Circumference

The circumference of a circle is the distance around the circle's edge or perimeter. It is calculated as 2πr, where r is the radius of the circle.

Relation between Rectangle and Perimeter

The perimeter of a rectangle is the distance around the rectangle's edge or boundary. It is calculated as 2(l + b), where l is the length and b is the breadth of the rectangle.

Comparison between Square and Diagonal

The diagonal of a square is the line segment connecting two opposite vertices of the square. It is calculated as √2 × side, where side is the length of the square's side.

However, there is no direct relationship between a square and diagonal, unlike the relationship between a circle and circumference, or a rectangle and perimeter.

Relation between Triangle and Area

The area of a triangle is calculated as 1/2 × base × height, where base is the length of the triangle's base and height is the perpendicular distance from the base to the opposite vertex.

Comparison between Plane and Dimension

A plane can have multiple dimensions, depending on the context. For example, a two-dimensional plane is a flat surface with only length and breadth, while a three-dimensional plane has length, breadth, and height.

There is no direct relationship between a plane and dimension, unlike the relationship between a circle and circumference or a rectangle and perimeter.

Conclusion

The correct answer to the given question is option D, Rectangle : Perimeter, as both rectangle and perimeter have a direct relationship, similar to the relationship between circle and circumference.