In measuring the sides of a rectangle , one side is taken 5% in excess, and the other 4% in deficit, Find the error percent in the area calculated from these measurements.
Question 2 Answer

a.
1.65%

b.
0.9%

c.
0.8%


d.
1%

Let the true length of the rectangle be \( L \) and the true breadth be \( B \).

- One side (length) is measured 5% in excess, so the measured length is \( 1.05L \).
- The other side (breadth) is measured 4% in deficit, so the measured breadth is \( 0.96B \).

Now, the actual area of the rectangle is \( A = L \times B \).

The measured area of the rectangle is:

\[
A_{\text{measured}} = (1.05L) \times (0.96B) = 1.05 \times 0.96 \times L \times B
\]

Simplifying:

\[
A_{\text{measured}} = 1.008 \times L \times B
\]

So the percentage error in the area is:

\[
\text{Error Percent} = \left( 1.008 - 1 \right) \times 100 = 0.008 \times 100 = 0.8\%
\]

Thus, the correct answer is:

**c. 0.8%**

Would you like further explanation or have any questions?

Here are 5 related questions to consider:
1. How do we calculate the percentage error for volume in a similar scenario?
2. What happens if both sides of the rectangle are measured in excess?
3. How do small measurement errors propagate in other geometric shapes?
4. What if both length and breadth had the same percentage error? Would the error in area still be the same?
5. How does the error change when percentage excess and deficit are equal?

**Tip:** For small percentage changes, the total percentage change in area can be approximately found by adding the percentage changes in length and width directly if they are small.

In measuring the sides of a rectangle, one side is taken 5% in excess, and the other 4% in deficit. Find the error percent in the area calculated from these measurements. a. 1.65% b. 0.9% c. 0.8% d. 1%

Learn how to calculate the percentage error in the area of a rectangle when one side is measured 5% in excess and the other side is measured 4% in deficit. This problem involves percentage error concepts and is suitable for students in Grades 8-10.

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