2026 · Q61
A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : ABCD is a rhombus of side 10 cm. What is the sum of the squares of the diagonals of the rhombus?
Statement IAC : BD = 3 : 4.
Statement IIAC = 6 cm.
Which one of the following is correct in respect of the above Question and Statements?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
- BThe Question can be answered by using either Statement alone.
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- DThe Question can be answered even without using both the Statements.
Explanation
For any rhombus, the parallelogram law gives AC² + BD² = 4 × (side)² = 4 × 100 = 400 cm², using only the given side of 10 cm. Neither statement is needed to answer the question, option D. (Statement I alone would also suffice via AC = 6k, BD = 8k with 100k² = 400, but the question is answerable even without the statements.)