Question

The percentage errors in the measurement of the length (L) and breadth (B) of a rectangle are $\ell andb$ respectively. Then the percentage error in the calculation of the area will be _____ .

• A. (lb)%
• B. (l+b)%
• C. (L+l)(B+b)
• D. Lb+BL

Answer 1

The correct option is B (l+b)%

Percentage error in length $\frac{\Delta L}{L}\times 100=l$%

Percentage error in breadth $\frac{\Delta B}{B}\times 100=b$%

Percentage error in area $\frac{\Delta A}{A}\times 100=\frac{\Delta L}{L}\times 100+\frac{\Delta B}{B}\times 100$

$⟹x\frac{\Delta A}{A}\times 100=(l+b)$%