4. The measurement of a side of a square is found to be 12 in. The possible error in measuring the side is .03 in. Approximate the error in computing the area of the square.
Unitary Method
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Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Problem Statement:**
The measurement of a side of a square is found to be 12 inches. The possible error in measuring the side is 0.03 inches. Approximate the error in computing the area of the square.
**Explanation:**
To approximate the error in the area, you may use the concept of differential error propagation. When the side of a square is measured as \( s \), the area \( A \) is given by:
\[ A = s^2 \]
The error in the area (\( \Delta A \)) can be approximated using the derivative of the area with respect to the side length (\( s \)) and the error in the side length (\( \Delta s \)):
\[ \Delta A = 2s \cdot \Delta s \]
Substitute the values:
- \( s = 12 \) inches
- \( \Delta s = 0.03 \) inches
The error in the area is:
\[ \Delta A = 2 \times 12 \times 0.03 \]
\[ \Delta A = 0.72 \text{ square inches} \]
Thus, the approximate error in computing the area of the square is 0.72 square inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18d66836-1cf9-4957-9659-b615a4dc4665%2F42fc0b2f-3e77-4925-b978-3f72c2f95a08%2Fgl1njng_processed.jpeg&w=3840&q=75)
Given:
The length of the side of the square is 12 in.
The possible error in the measurement is 0.03 in.
That is, the length of the square is
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