Question

Area of rectangular field is A=l×b,where l = (200 +_ 5) m and b is (50 +_ 2)m. Find the percentage error in A

Answer 1

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

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 %

Answer 2

Answer:

The percentage error in A is 6.5%.

Explanation:

Given that,

Length $l =(200\pm5)\ m$

Breadth $b=(50\pm2)\ m$

Area of rectangular field is

$A=l\times b$

The formula of the percentage error is define as:

$\dfrac{\Delta A}{A}=\dfrac{\Delta l}{l}+\dfrac{\Delta b}{b}$

$\dfrac{\Delta A}{A}\times100=\dfrac{5}{200}\times100+\dfrac{2}{50}\times100$

$\dfrac{\Delta A}{A}\times100=2.5+4$

$\dfrac{\Delta A}{A}\times100=6.5\%$

Hence, The percentage error in A is 6.5%.