The measured dimensions of a shape or a solid are given to the nearest whole unit. Find the greatest percent error of each shape or solid.
The perimeter of a rectangle with length
To find : the greatest percent error perimeter of rectangle.
Answer to Problem 28P
0.3%
Explanation of Solution
Given information: The length and width of rectangle are 127 ft and 211ft when measured to the nearest ft
Calculation:
Perimeter of the rectangle with length and width are 127 ft and 211ft when measured to the nearest ft is
The measurement was made to the nearest ft , so the greatest possible error is half of 1ft, that is 0.5 ft.
Therefore, minimum measurement of length and width of the rectangle are (127-0.5) ft by (211-0.5) ft, that is 126.5 ft by 210.5 ft respectively.
And maximum measurement of the dimensions of the rectangle are ((127+0.5) ft by (211+0.5) ft, that is 127.5 ft by 211.5 ft respectively.
Therefore, minimum possible perimter of the rectangle is
And maximum possible perimeter of the rectangle is
Now, absolute value of difference of perimeter P and
Therefore, greatest percentage error in perimeter of rectangle =
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