While measuring the side of an equilateral triangle an error of k % is made, the percentage error in its area is

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KollegeApply · Accepted Answer

2k% Let x be the side of the triangle and y be its area. ∆ x/x $\times$ 100 = k \text { Also }, y = $\sqrt$(3)/4 x^2 \Rightarrow dy/dx = $\sqrt$(3)/2x \Rightarrow ∆ y/y = $\sqrt$(3)x/2ydx = 2/x $\times$ kx/100 \Rightarrow ∆ y/y $\times$ 100 = 2k \text { Hence, the error in the area of the triangle is } 2k . %

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