Question

Three students Varun, Kartik and Sid wrote a statement on a blackboard.
Varun wrote, “Two rectangles are congruent, if they have same perimeter”.
Kartik wrote, “Two squares are congruent, if they have same area”.
Sid wrote, “Two circles are congruent, if they have same diameter”.
Who wrote the correct statement?

• A. Varun, Kartik and Sid
• B. Kartik and Sid
• C. Varun and Kartik
• D. Varun and Sid

Answer 1

The correct option is B Kartik and Sid

Varun statement: Two rectangles are congruent, if they have same perimeter.
Two rectangles having same perimeter can not be congruent beacuse lenght and width of rectangle may vary.
For example:
If l = 4 cm , b = 2 cm then perimeter will be 12 cm
and if l = 1 cm, b = 5 cm then also perimeter will be 12 cm.
So, if perimeter of two rectangles is same then also it is not necessary that both rectangles will be congruent.

Kartik statement: Two squares are congruent, if they have same area.
If two squares have the same area, then both squares will be congruent because in square, all sides are equal.

Sid statement: Two circles are congruent, if they have same diameter.
Circle will be of fixed shape if diametres or radius are same.
Hence, circles of same diameter are congruent.

Therefore, Kartik and Sid wrote right statement.