To solve the problem, we calculate the percent error in the area of the rectangle due to potential measurement errors. Here is how we approach it:

Step 1: Area Formula

The area $A$ of a rectangle is given by: $A = \text{length} \times \text{width}$

For the given rectangle: $A = 17 \, \text{yd} \times 15 \, \text{yd} = 255 \, \text{yd}^2$

Step 2: Percent Error Formula

The percent error in area is approximated by adding the relative percent errors in the length and width measurements.

If the relative error in the length is $e_1 \%$ and the relative error in the width is $e_2 \%$, then the total percent error in the area is: $\text{Total Error} \approx e_1 + e_2$

Step 3: Interpret Measurement Error

Since no specific error values are given for the dimensions, assume standard measurement error of $1 \, \text{yd}$ for each dimension. The relative errors are: $e_1 = \frac{\text{Error in Length}}{\text{Length}} \times 100 = \frac{1}{17} \times 100 \approx 5.88\%$ $e_2 = \frac{\text{Error in Width}}{\text{Width}} \times 100 = \frac{1}{15} \times 100 \approx 6.67\%$

Step 4: Add Percent Errors

Add the relative errors to find the total percent error in the area: $\text{Total Error} \approx 5.88\% + 6.67\% = 12.55\%$

Rounded to the nearest tenth: $\text{Total Error} = 12.6\%$

Final Answer:

The percent error in the calculated area is: $\boxed{12.6\%}$

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Related Questions:

1. What is the formula to calculate area percent error for more precise measurement errors?
2. How does increasing the error margin in the dimensions affect the total area percent error?
3. If one dimension had zero error, how would the percent error in area be calculated?
4. How does rounding affect the accuracy of the percent error calculation?
5. How does the error propagation differ for shapes other than rectangles?

Tip:

Always calculate relative errors for each dimension separately before summing them to approximate the overall area error.