Question

The measured dimensions of a rectangle are 7m by 4m to the nearest whole unit. Find the minimum and maximum possible areas of the rectangle

Answer 1

The minimum area of the rectangle is 22.75m² found by multiplying 6.5m and 3.5m, and the maximum area is 32.56m², calculated from 7.4m by 4.4m.

Step-by-step explanation:

The measured dimensions of a rectangle are 7m by 4m to the nearest whole unit. To find the minimum and maximum possible areas of the rectangle, we need to consider the smallest and largest values that could round to 7m and 4m, respectively. Since the measurements are rounded to the nearest whole meter, the minimum possible length could be 6.5m (just over 6m when rounded), and the maximum would be 7.4m (just under 7.5m when rounded) for the length. Similarly, the width could be as little as 3.5m and as much as 4.4m.

Calculating the minimum area, we multiply the smallest possible length and width: 6.5m x 3.5m = 22.75m².

The maximum area is found by multiplying the largest possible length and width: 7.4m x 4.4m = 32.56m².

Thus, the minimum possible area of the rectangle is 22.75m², and the maximum possible area is 32.56m².

Answer 2

Maximum area = Minimum area = 28 m².

Step-by-step explanation:

The length and the width of the rectangle are measured to be 7 m and 4 m respectively to the nearest whole number.

We have to find the maximum and minimum possible areas of the rectangle.

The maximum or minimum area is calculated only when length or width or both can vary and then only for a certain value of length and width the area becomes maximum or minimum.

So, the maximum and minimum area of the rectangle will be the same i.e. (7 × 4) = 28 m². (Answer)