2026 · Q62
A Question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : The diagonal of a rectangle ABCD (AB > BC) is 5√2 cm. What is its perimeter?
Statement ILength AB is an integer.
Statement IILength BC is an integer.
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
With diagonal 5√2, AB² + BC² = 50 and AB > BC. Statement I alone (AB integer) admits both (AB, BC) = (7, 1) and (6, √14); statement II alone (BC integer) admits several pairs too — neither fixes the perimeter. With both, AB and BC integers satisfying AB² + BC² = 50 and AB > BC forces (AB, BC) = (7, 1), so the perimeter is 16 cm. Both statements together, but neither alone, option C.