Chapter 2.10, Problem 25P

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

$4\text{cm}$ by $7\text{cm}$

To determine

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

Answer to Problem 25P

Minimum and maximum possible area of the rectangle are 22.75 square cm and 33.75 square cm respectively.

Explanation of Solution

Given information: The measured dimensions of the rectangle are 4 cm by 7 cm to the nearest cm.

Calculation:

The degree of accuracy is half a unit of measure.

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

Therefore, minimum measurement of the dimensions of the rectangle are (4-0.5) cm by (7-0.5) cm, that is 3.5 cm by 6.5 cm.

And maximum measurement of the dimensions of the rectangle are (4+0.5) cm by (7+0.5) cm, that is 4.5 cm by 7.5 cm.

Therefore, minimum possible area of the rectangle is

  $A_{\min }=3.5\times 6.5=22.75c{m}^2$

And maximum possible area of the rectangle is

  $A_{\max }=4.5\times 7.5=33.75c{m}^2$

Thus, minimum and maximum possible area of the rectangle are 22.75 square cm and 33.75 square cm respectively.