Question

Q24. Area of rectangular field A = 1 x b, where I = (2005)m and
b = (500+2)m. Find the percentage error in A.​

Answer 1

Answer:

6.5%

Explanation:

Relation between Area (A), Length (l) and breadth (b) is given by

A = l × b

differentiate both sides,

dA = b × dl + l × db

dividing by A both sides,

dA/A = b × dl/A + l × db/A

dA/A = b × dl/l × b + l × db/l × b

dA/A = dl/l + db/b

Hence , for finding error we have expression

\boxed{\boxed{\bold{\frac{\Delta{A}}{A}=\frac{\Delta{l}}{l}+\frac{\Delta{b}}{b}}}}

A

ΔA

=

l

Δl

+

b

Δb

Given, l = (200 ± 5) m and b = (50 ± 2)m

so, A = 200 × 5 = 1000

∆l = 5, ∆b = 2

We have to find % error ,

e.g., we have to find ∆A/A × 100 = ?

Now, ∆A/A = 5/200 + 2/50

Multiply 100 in both sides,

∆A/A × 100 = 5/200 × 100 + 2/50 × 100

% error = 5/2 + 4 = 2.5 + 4 = 6.5 %

Hence, percentage error in A = 6.5 %