Question

13.) a contractor has a blueprint for the foundation of a building. the measurements are 35 ft by 20 ft. once the building was complete, the actual measurements were 35.3 ft by 20.9 ft.
a. find the percent error of the perimeter from the blueprint to the actual building.
b. find the percent error of the area from the blueprint to the actual building.
hint: $a = lw$

Explanation:

Step1: Calculate blueprint perimeter

$P_{blueprint} = 2\times(35 + 20) = 2\times55 = 110$ ft

Step2: Calculate actual perimeter

$P_{actual} = 2\times(35.3 + 20.9) = 2\times56.2 = 112.4$ ft

Step3: Find perimeter error amount

$|P_{actual} - P_{blueprint}| = |112.4 - 110| = 2.4$ ft

Step4: Calculate perimeter percent error

$\text{Percent Error (Perimeter)} = \frac{2.4}{110} \times 100\% \approx 2.18\%$

Step5: Calculate blueprint area

$A_{blueprint} = 35\times20 = 700$ ft²

Step6: Calculate actual area

$A_{actual} = 35.3\times20.9 = 737.77$ ft²

Step7: Find area error amount

$|A_{actual} - A_{blueprint}| = |737.77 - 700| = 37.77$ ft²

Step8: Calculate area percent error

$\text{Percent Error (Area)} = \frac{37.77}{700} \times 100\% \approx 5.40\%$

Answer:

a. The percent error of the perimeter is approximately 2.18%
b. The percent error of the area is approximately 5.40%