Given below are two statements:
Statement I : Only one rhombus ABCD can be drawn with AB = 4 cm and diagonal BD = 5 cm
Statement II : Only one parallelogram ABCD can be drawn with AB = 6 cm and diagonal BD = 8 cm
In the light of the above statements, choose the correct answer from the options given below
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Statement I is true but statement II is false
A quadrilateral is fixed (only one can be drawn) when the data fix the triangle formed by two sides and the diagonal between them. A triangle is fixed by its three sides; with only two sides known, it can be drawn in many shapes.
Statement I : Only one rhombus ABCD can be drawn with AB = 4 cm and diagonal BD = 5 cm Correct. All sides of a rhombus are equal, so AD = AB = 4 cm. Triangle ABD has all three sides known (4 cm, 4 cm, 5 cm), so it has one shape, and C is then fixed (CB = CD = 4 cm on the other side of BD).
Statement II : Only one parallelogram ABCD can be drawn with AB = 6 cm and diagonal BD = 8 cm Incorrect. In a parallelogram the side AD need not equal AB, and it is not given. Triangle ABD has only two sides known, so D can be placed in many positions 8 cm from B, giving many different parallelograms.
