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If the error in measuring the side $l$ of an equilateral triangle is 0.01 , then the percentage error in the area of the triangle, in terms of its side $l$ is
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1423 Upvotes
Verified Answer
The correct answer is:
$\frac{2}{1}$
Given,
$$
d l=0.01
$$
Area of equilateral triangle i.e.
$$
A=\frac{\sqrt{3}}{4} l^2
$$
$\Rightarrow \quad \frac{d A}{d l}=\frac{\sqrt{3}}{2} l$
$$
\begin{aligned}
& \frac{d A}{A} \times 100=\frac{\sqrt{3}}{2} \frac{l d l}{A} \times 100 \\
& \frac{d A}{A} \times 100=\frac{\sqrt{3} l}{2 \times \frac{\sqrt{3}}{4} l^2} \times 0.01 \times 100 \\
& \frac{d A}{A} \times 100=\frac{2}{l}
\end{aligned}
$$
$\therefore$ Percentage in area of triangle is $\frac{2}{l}$.
$$
d l=0.01
$$
Area of equilateral triangle i.e.
$$
A=\frac{\sqrt{3}}{4} l^2
$$
$\Rightarrow \quad \frac{d A}{d l}=\frac{\sqrt{3}}{2} l$
$$
\begin{aligned}
& \frac{d A}{A} \times 100=\frac{\sqrt{3}}{2} \frac{l d l}{A} \times 100 \\
& \frac{d A}{A} \times 100=\frac{\sqrt{3} l}{2 \times \frac{\sqrt{3}}{4} l^2} \times 0.01 \times 100 \\
& \frac{d A}{A} \times 100=\frac{2}{l}
\end{aligned}
$$
$\therefore$ Percentage in area of triangle is $\frac{2}{l}$.
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