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an error 2% in excess is made while measuring the side of a square. the percentage of error in the calculated area of the square is: a) 2% b) 4% c) 4.04% d) 2.02%

User Zymawy
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Answer: C

Explanation:

To find the percentage of error in the calculated area of the square when there is a 2% error in measuring its side, you can use the formula for the area of a square:

Area = side × side

Let's assume the actual side of the square is "S," and the measured side with a 2% error is "S_actual."

Given that there's a 2% error in measuring the side, we have:

S_actual = S + 0.02S

Now, let's calculate the area with the actual side and the measured side:

Actual Area = S × S

Measured Area = S_actual × S_actual = (S + 0.02S) × (S + 0.02S) = S^2 + 0.04S^2 + 0.0004S^2

Now, let's find the percentage error in the calculated area:

Percentage Error = [(Measured Area - Actual Area) / Actual Area] × 100

Percentage Error = [(S^2 + 0.04S^2 + 0.0004S^2 - S^2) / S^2] × 100

Percentage Error = [(0.04S^2 + 0.0004S^2) / S^2] × 100

Percentage Error = [(0.0404S^2) / S^2] × 100

Percentage Error = 4.04%

So, the percentage of error in the calculated area of the square is 4.04%, which corresponds to option (c).

User DANG Fan
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