Given below are two statements:

**Statement I:** Only one Rhombus ABCD can be drawn with $$ AB = 4 \, ext{cm} $$ and diagonal $$ BD = 5 \, ext{cm} $$.
**Statement II:** Only one parallelogram ABCD can be drawn with $$ AB = 6 \, ext{cm} $$ and diagonal $$ BD = 8 \, ext{cm} $$.

In the light of the above statements, choose the correct answer from the options given below:

Question

Given below are two statements:

**Statement I:** Only one Rhombus ABCD can be drawn with $$ AB = 4 \, 	ext{cm} $$ and diagonal $$ BD = 5 \, 	ext{cm} $$.  
**Statement II:** Only one parallelogram ABCD can be drawn with $$ AB = 6 \, 	ext{cm} $$ and diagonal $$ BD = 8 \, 	ext{cm} $$.

In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

To analyze the statements:

**Statement I:**  
For a rhombus, all sides are equal, and the diagonals bisect each other at right angles. Given $$ AB = 4 \, 	ext{cm} $$ and diagonal $$ BD = 5 \, 	ext{cm} $$:  
- Half of diagonal $$ BD = 2.5 \, 	ext{cm} $$. Using the Pythagoras theorem in triangle $$ AOB $$:  
  $$
  AO^2 = AB^2 - OB^2 = (4)^2 - (2.5)^2 = 16 - 6.25 = 9.75
  $$
  Thus, $$ AO = \sqrt{9.75} = 3.1225 $$.  
- The full length of diagonal $$ AC = 2 	imes AO = 6.245 \, 	ext{cm} $$.

Since all conditions for a rhombus are satisfied and only one unique rhombus can be formed with these dimensions, **Statement I is true**.

**Statement II:**  
For a parallelogram, knowing only one side ($$ AB = 6 \, 	ext{cm} $$) and one diagonal ($$ BD = 8 \, 	ext{cm} $$) is insufficient to uniquely determine its shape. A parallelogram requires additional information such as angles or both diagonals for unique construction. Hence, **Statement II is false**.

Thus, the correct answer is **(c)**: Statement I is true but Statement II is false.

Answer

Answer

Answer