2026 · Q62
A square and a rectangle have the same perimeter p and their areas differ by q units. What is the square of the difference between the length and breadth of the rectangle?
Elementary MathematicsMensuration
- A1.5q
- B2q
- C2.5q
- D4q
Explanation
The square has side p/4 and area p²/16; the rectangle has ℓ+b=p/2 and ℓb=p²/16−q. Then (ℓ−b)²=(ℓ+b)²−4ℓb=p²/4−4(p²/16−q)=4q, option D. Geometrically, (ℓ−b)² measures how far the rectangle deviates from the square of equal perimeter.