Question

Statement (1): A rhombus shaped sheet with perimeter 40 cm has one diagonal 12 cm the other diagonal is 16 cm.

Statement (2): If the other diagonal of this rhombus = x cm, x = 10² – 6².

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 is true because the rhombus has side 10 cm and diagonals 12 cm and 16 cm, which satisfy \[6^2 + 8^2 = 10^2\]. Statement 2 is false because equating x directly to \[10^2 - 6^2\] is dimensionally incorrect (the correct relation is \[\left(\frac{x}{2}\right)^2 = 10^2 - 6^2\]).