Chapter 2.10, Problem 29P

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 determine

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

  $A=14\times 11=154i{n}^2.$

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

  $A_{\min }=13.5\times 10.5=141.75i{n}^2.$

And maximum possible area of the rectangle is

  $A_{\max }=14.5\times 11.5=166.75i{n}^2.$

Now, absolute value of difference of areas A and $A_{\min }$ is 12.25 in². and absolue value of difference of area A and

  $A_{\max }$ is 12.75 in².

Therefore, greatest percentage error in area of rectangle = $\frac{12.75}{154}\times 100=8.3\%$