Two rectangular pieces of land, both having all sides and diagonals in whole numbers (in meters), have areas in the ratio 4:3. The smaller piece has a diagonal of 41m and one side of 9m. However, the bigger piece has a smaller diagonal. The diagonal of the bigger piece is:

Correct option is D

Given:
· Ratio of areas = 4:3
· Smaller rectangle:
· Diagonal = 41m
· One side = 9m
· Bigger rectangle has a smaller diagonal
The smaller rectangle has a diagonal of 41m and one side of 9m. Using the Pythagorean theorem:
412=92+b2
1681 = 81 + b²
b² = 1600 → b = 40
So, the dimensions of the smaller rectangle are 9m × 40m.
The areas are in the ratio 4:3, so the bigger rectangle’s area is:
(x × y) / (9 × 40) = 4/3
x × y = (4/3) × 360 = 480
Possible integer dimensions are 16 × 30.
The diagonal of the bigger rectangle:
d = √(16² + 30²)
d = √(256 + 900)
d = √1156 = 34.
Since the bigger rectangle has a smaller diagonal, the answer is (d) 34.