An error 2% in excess is made while measuring the side of a

[nkmungila1]

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. 2.02%
C. 4%
D. 4.04%
E. 40.4 %

[ErikaPrepScholar]

Let's say that the actual length of one side of the square is x. This means that the actual area of the square is x^2.

If we made a 2% error in excess in measuring the length of the side, we measured the side to be 102% of how long it actually is. Converting this into a decimal, we get that 102% of x = 1.02x. This means that the area we calculated for the square is (1.02x )^2 or 1.0404x^2.

So the area of the square we calculated is 1.0404 times the actual area of the square, or 104.04% of the actual area of the square. This is an excess of 4.04%, meaning that the correct answer is D.

[Scott@TargetTestPrep]

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. 2.02%
C. 4%
D. 4.04%
E. 40.4 %

We can let the side of the square = 100. The erroneous side is 2% in excess, so the erroneous side = 102. The area of the square is supposed to be 100^2 = 10,000, but the erroneous square has an area of 102^2 = 10,404. Therefore, the percentage of error in the calculated area of the square is:

(10,404 - 10,000)/10,000 x 100 = 404/100 = 4.04 percent

Answer: D