A rectangular lawn was measured to have a length of 15.0\text{ m} and a width of 8.0\text{… — JAMB UTME

A rectangular lawn was measured to have a length of $15.0\text{ m}$ and a width of $8.0\text{ m}$ . If the actual length of the lawn is $16.0\text{ m}$ and the measured width is exact, what is the percentage error in the calculated area of the lawn?

Answer: 6.25 %

Answer

The percentage error in the calculated area is

6.25\%

The actual area of the lawn is

16.0\text{ m} \times 8.0\text{ m} = 128\text{ m}^2

, while the measured area is

15.0\text{ m} \times 8.0\text{ m} = 120\text{ m}^2

. The error is

128 - 120 = 8\text{ m}^2

. Expressed as a percentage of the actual area,

\frac{8}{128} \times 100\% = 6.25\%

Step-by-Step Solution

Calculate the measured area of the lawn using the measured length and width

\text{Measured Area} = 15.0\text{ m} \times 8.0\text{ m} = 120\text{ m}^2

Area of a rectangle is length multiplied by width.

Calculate the true (actual) area of the lawn using the actual length and exact width

\text{Actual Area} = 16.0\text{ m} \times 8.0\text{ m} = 128\text{ m}^2

The actual dimensions determine the true surface area.

Determine the magnitude of the error in area

\text{Error} = |128\text{ m}^2 - 120\text{ m}^2| = 8\text{ m}^2

Error is defined as the absolute difference between actual and measured values.

Compute the percentage error relative to the actual area

\text{Percentage Error} = \frac{8}{128} \times 100\% = 6.25\%

Percentage error is always calculated as

\frac{\text{Error}}{\text{Actual Value}} \times 100\%

Key Concept

Percentage Error Calculation in Compound Quantities

Estimated Time:1m 30s

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