2018 · Q92
The product of the lengths of the diagonals of a square is 50 square units. What is the length of a side of the square?
Elementary MathematicsQuadrilaterals and Polygons
- A5√2 units
- B5 units
- C10 units
- D2√5 units
Explanation
In a square of side s, each diagonal has length s√2 by Pythagoras. The product of the two diagonals is therefore s√2 × s√2 = 2s². Setting 2s² = 50 gives s² = 25, so s = 5 units (lengths are positive). The distractor 5√2 units is the diagonal's length, not the side — a common mix-up. Hence option (B) 5 units.