While measuring the side of an equilateral triangle an error of `k %` is made, the percentage error in its area is `k %` (b) `2k %` (c) `k/2%` (d) `3k %`

Explanation

Correct option is B)

Area of equilateral triangle `{A}=frac{sqrt{3}}{4} {x}^{2}` `frac{{dA}}{{dx}}=frac{sqrt{3}}{2} {x}`

Given, percentage error in measuring side `={k} %`

`Rightarrow frac{Delta {x}}{{x}}=frac{{k}}{100} `

`Rightarrow Delta {x}=frac{{kx}}{100}`


Now, approximate error in measuring `{A}={dA}=(frac{{dA}}{{dx}}) Delta {x}`


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