We read your photo as:

Determine the nominal perimeter.

Mathematics

ScanSolve AI Answer

Answer

0.5%0.5\%

Step-by-step solution

4 steps
  1. Determine the nominal perimeter.

    The length of the room is L=12.0L = 12.0 m and the width is W=8.0W = 8.0 m.
    The nominal perimeter P0P_0 is given by the formula P=2(L+W)P = 2(L + W).

    P0=2(12.0+8.0)=2(20.0)=40.0 mP_0 = 2(12.0 + 8.0) = 2(20.0) = 40.0 \text{ m}
  2. Determine the absolute error in length and width.

    Since the measurements are given to one decimal place (e.g., 12.0 m, 8.0 m), the maximum possible absolute error for each measurement is half of the smallest unit, which is 0.1 m.
    Absolute error in length, ΔL=0.12=0.05\Delta L = \frac{0.1}{2} = 0.05 m.
    Absolute error in width, ΔW=0.12=0.05\Delta W = \frac{0.1}{2} = 0.05 m.

  3. Calculate the maximum absolute error in the perimeter.

    The perimeter P=2(L+W)P = 2(L + W). The maximum absolute error in the perimeter, ΔP\Delta P, is the sum of the absolute errors in length and width, multiplied by 2.

    ΔP=2(ΔL+ΔW)\Delta P = 2(\Delta L + \Delta W) ΔP=2(0.05+0.05)\Delta P = 2(0.05 + 0.05) ΔP=2(0.10)\Delta P = 2(0.10) ΔP=0.20 m\Delta P = 0.20 \text{ m}
  4. Calculate the maximum percentage error.

    The maximum percentage error is given by the formula:

    Percentage Error=Maximum Absolute ErrorNominal Value×100%\text{Percentage Error} = \frac{\text{Maximum Absolute Error}}{\text{Nominal Value}} \times 100\% Percentage Error=ΔPP0×100%\text{Percentage Error} = \frac{\Delta P}{P_0} \times 100\% Percentage Error=0.2040.0×100%\text{Percentage Error} = \frac{0.20}{40.0} \times 100\% Percentage Error=0.005×100%\text{Percentage Error} = 0.005 \times 100\% Percentage Error=0.5%\text{Percentage Error} = 0.5\%

    The maximum percentage error in estimating the perimeter of the room is 0.5%\boxed{0.5\%}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp