Question

Statement (1): For a quadrilateral ABCD, if AB = BC = CD = DA = 8 cm, then it is possible to construct this quadrilateral.

Statement (2): It is only possible to construct this quadrilateral if each of its diagonals is greater than 8 cm.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is true, and statement 2 is false.

Explanation:

• Statement (1): Given four equal sides of length 8 cm, a rhombus (or equilateral quadrilateral) can be drawn, making Statement (1) true.
• Statement (2): In a rhombus with side length 8 cm, the diagonals can vary in length depending on the interior angles (for instance, when an interior angle is less than 60°, the shorter diagonal is less than 8 cm). Therefore, it is incorrect to state that diagonals must strictly be greater than 8 cm, making Statement (2) false.