Question

Mar 01, 9:31:07 PM The actual dimensions of a rectangle are 8cm by 6cm. Alex measures the sides to be 7.91cm by 5.95cm. In calculating the area, what is the relative error, to the nearest hundredth.

Answer 1

To calculate the relative error in calculating the area of the rectangle, subtract the measured area from the actual area and divide by the actual area. Rounded to the nearest hundredth, the relative error is 0.02 (or 2%).

Step-by-step explanation:

To calculate the relative error in calculating the area of the rectangle, we'll compare the actual area with the measured area. The actual area is 8cm × 6cm = 48cm². The measured area is 7.91cm × 5.95cm = 47.0745cm². Subtracting the measured area from the actual area gives us the absolute error: 48cm² - 47.0745cm² = 0.9255cm².

To find the relative error, we'll divide the absolute error by the actual area: 0.9255cm² / 48cm² = 0.019282.

Rounding the relative error to the nearest hundredth gives us a final answer of 0.02. Therefore, the relative error in calculating the area of the rectangle is 0.02 (or 2%).