Answer :
Given Data:
- The difference in length between the larger square and the smaller square is 24 m.
- The uncovered area is 1920 m².
Steps to Solve:
1. Let the side length of the smaller square be x.
2. Then, the side length of the larger square will be x + 24 m.
3. Calculate the area of both squares:
Area of the smaller square (A) = x²
Area of the larger square (B) = (x + 24)²
4. Calculate the area of the uncovered region:
Uncovered area = Area of (larger square − smaller square)=1920m²
5. Set up the equation:
(x + 24)² − x² = 1920
6. Expand and simplify the equation:
x² + 48x + 576 − x² = 1920
48x + 576 = 1920
7. Solve for x :
48x = 1920 − 576
48x = 1344
x = 28m
Conclusion:
- The side length of the small square A is 28 m.