Chapter 2.10, Problem 26P

The measured dimensions of a rectangle are given to the nearest whole unit. Find the minimum and maximum possible areas of each rectangle.

$16\text{ft}$ by $15\text{ft}$

To determine

To find : the minimum and maximum possible area of the rectangle. .

Answer to Problem 26P

Minimum and maximum possible area of the rectangle are 224.75 square ft and 255.75 square ft respectively.

Explanation of Solution

Given information: The measured dimensions of the rectangle are 16 ft by 15 ft to the nearest ft.

Calculation:

The degree of accuracy is half a unit of measure.

The measurement was made to the nearest ft , so the greatest possible error is half of 1 ft, that is 0.5 ft.

Therefore, minimum measurement of the dimensions of the rectangle are (16-0.5) ft by (15-0.5) ft, that is 15.5 ft by 14.5

And maximum measurement of the dimensions of the rectangle are (16+0.5) ft by (15+0.5) ft, that is 16.5 ft by 15.5 ft.

Therefore, minimum possible area of the rectangle is

  $A_{\min }=15.5\times 14.5=224.75f{t}^2$

And maximum possible area of the rectangle is

  $A_{\max }=16.5\times 15.5=255.75f{t}^2$

Thus, minimum and maximum possible area of the rectangle are 224.75 square ft and 255.75 square ft respectively.