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 area of a rectangle with length 14 in. and width 11 in.
To find : the greatest percent error of the area of rectangle.
Answer to Problem 29P
8.3
Explanation of Solution
Given information: The length and width of rectangle are 14 in. and 11 in. when measured to the nearest inch.
Calculation:
Area of the rectangle with length and width are 14 in. and 11 in. when measured to the nearest inch is
The measurement was made to the nearest inch , so the greatest possible error is half of 1 in., that is 0.5 in.
Therefore, minimum measurement of length and width of the rectangle are (14-0.5) in. by (11-0.5) in., that is 13.5 in. by 10.5 in. respectively.
And maximum measurement of the dimensions of the rectangle are (14+0.5) in. by (11+0.5) ft, that is 14.5 in. by 11.5 in. respectively.
Therefore, minimum possible area of the rectangle is
And maximum possible area of the rectangle is
Now, absolute value of difference of areas A and
Therefore, greatest percentage error in area of rectangle =
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