Percentage Change in Length of Rectangle given Percentage Change in Area and Breadth Calculator

Formula Used:

\[ \text{Percentage Change in Length of Rectangle} = \left( \frac{1 + \frac{\text{Percentage Change in Area of Rectangle}}{100}}{1 + \frac{\text{Percentage Change in Breadth of Rectangle}}{100}} - 1 \right) \times 100 \]

Percentage Change in Length of Rectangle:

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1. What is Percentage Change in Length of Rectangle?

Percentage Change in Length of Rectangle measures the relative change in the length dimension of a rectangle when both the area and breadth undergo percentage changes. It helps understand how one dimension adjusts when others change proportionally.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Percentage Change in Length} = \left( \frac{1 + \frac{\text{Area Change \%}}{100}}{1 + \frac{\text{Breadth Change \%}}{100}} - 1 \right) \times 100 \]

Where:

Area Change % — Percentage change in the area of the rectangle
Breadth Change % — Percentage change in the breadth of the rectangle

Explanation: The formula calculates how the length must change proportionally to maintain the area-breadth-length relationship when both area and breadth experience percentage changes.

3. Importance of Length Change Calculation

Details: This calculation is crucial in geometry, engineering design, and material science where dimensional relationships must be maintained when scaling objects or dealing with thermal expansion/contraction.

4. Using the Calculator

Tips: Enter both percentage changes as numbers (positive for increase, negative for decrease). The calculator will compute the required percentage change in length to maintain the proportional relationship.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive result indicate?
A: A positive result indicates that the length must increase to accommodate the changes in area and breadth while maintaining proportionality.

Q2: What does a negative result indicate?
A: A negative result indicates that the length must decrease to maintain the proportional relationship between area, breadth, and length.

Q3: Can this formula handle decimal percentages?
A: Yes, the calculator accepts decimal values for precise calculations of percentage changes.

Q4: What if both area and breadth change by the same percentage?
A: If area and breadth change by the same percentage, the length change will be 0%, maintaining the original proportions.

Q5: How is this calculation useful in real-world applications?
A: This is useful in manufacturing, construction, and design where materials expand/contract with temperature changes, requiring proportional adjustments in dimensions.