The width of a rectangle is measured as 12.3 cm, while the length is measured as 28.8 cm. The width measurement could be off by 1.2 cm, and the length could be off by .04 cm. Estimate the maximum possible error in calculating the area of the rectangle.
width is between 11.1 and 13.5 cm\length is between 28.76 and 28.84 cm
area is thus between 319.236 and 389.34 cm^2
That's 354.288 ± 35.052 cm^2
use correct significant digits
Thanks, that's the answer I get.
To estimate the maximum possible error in calculating the area of the rectangle, we need to consider the effect of the measurement errors for both the width and the length.
The area of a rectangle is calculated by multiplying the length and the width: A = length × width.
Let's first consider the effect of the width measurement error. The actual width could be anywhere from 12.3 cm - 1.2 cm = 11.1 cm to 12.3 cm + 1.2 cm = 13.5 cm.
Next, let's consider the effect of the length measurement error. The actual length could be anywhere from 28.8 cm - 0.04 cm = 28.76 cm to 28.8 cm + 0.04 cm = 28.84 cm.
Now, we can calculate the possible minimum and maximum areas of the rectangle.
The minimum area occurs when the width and length take their smallest possible values: A_min = 11.1 cm × 28.76 cm.
The maximum area occurs when the width and length take their largest possible values: A_max = 13.5 cm × 28.84 cm.
To estimate the maximum possible error, we can find the difference between the maximum and minimum areas: max_error = A_max - A_min.
Substituting the values, we have:
max_error = (13.5 cm × 28.84 cm) - (11.1 cm × 28.76 cm)
Calculating this gives us the estimated maximum possible error in calculating the area of the rectangle.