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The dimensions of a square is given as 6.25 cm. A student measured one side of the square as 6.12 cm to calculate
the perimeter and the area of the square. Find the percentage error in:
i. Measured length
ii. Calculated perimeter
iii. Calculated area
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This problem is a standard 6-grade exercise for ratio and percentage.
Therefore, I solve it at the appropriate level using elementary algebra
with complete explanations and without involving other approaches.
In this problem, we are given the precise value of the side of the square as 6.25 cm,
and we also are given some measured value of the side of the square,
which represents some deviation from the precise value.
For part (iii), we should calculate the deviation as the difference
measured value the precise value. (1)
In this case, we have no measured value for the area, but we can compute it as the square
of the measured side, 6.12^2 cm^2.
So, doing it in the course of formula (1), we calculate the deviation of the computed area as
computed area 6.12^2 cm^2 MINUS the precise area 6.25^2 cm^2, or 6.12^2 - 6.25^2 = -1.6081 cm^2.
Then we relate this found deviation of the area to the EXACT GIVEN value of the area.
Doing this way, we obtain
= -0.04116736 = -0.041167 (rounded), or -4.1167%.
The sign " minus " here points that the measured/computed area is less than the precise value.
But since the problem asks about the " error ", it instructs us to take the absolute value
of the calculated "percentage of the deviation".
So, the correct answer for (iii) is 4.1167% (the positive value).
Solved.
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Notice that in such problems, choosing and using a correct treatment
is of a principial importance, and it does not allow to split or to double or to modify the interpretation.
The whole wisdom in solving such problems is that if the precise value is given,
then we should calculate the percentage of the deviation using the formulas centered around this precise given value;
then we should take the absolute value for the final " error value ".
Thus, in accordance with the problem intention/purpose, this my post TEACHES you
to interpret the problem correctly at the 6-grade level, and also TEACHES you to choose and to use
ONE single UNIQUE CORRECT interpretation for this level
and work with it /(follow it) it from the beginning to the end.