How to Find Percentage Change in Perimeter?

Percentage Change in Perimeter measures how much a figure’s perimeter increases or decreases compared with its original perimeter. The calculation uses the original and new perimeter values. For rectangles and squares, changes in side lengths can also be used directly to find the new perimeter and its percentage change.

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What Is Percentage Change in Perimeter?

Percentage change in perimeter is the change from the original perimeter expressed as a percentage of the original perimeter.

The formula is (New Perimeter − Original Perimeter) ÷ Original Perimeter × 100. A positive result shows an increase, while a negative result shows a decrease. For example, if the perimeter changes from 40 cm to 50 cm, the percentage change is (50 − 40) ÷ 40 × 100 = 25%.

Percentage Change in Perimeter Video Lessons

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Percentage Change in Area and Perimeter

Learn how to solve percentage-based questions involving changes in the area and perimeter of two-dimensional figures using appropriate mensuration formulas.

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Percentage Change in Perimeter Formula & Tricks

Important Formulas

Percentage change in perimeter
Percentage change = [(New perimeter − Original perimeter) ÷ Original perimeter] × 100

Use the original perimeter as the denominator. The result is positive for an increase and negative for a decrease.

Rectangle perimeter
P = 2(l + b)

Here, l is the length and b is the breadth of the rectangle.

Square perimeter
P = 4a

Here, a is the side length of the square.

Equal percentage change in all linear dimensions
If every length is multiplied by k, new perimeter = k × original perimeter

Since perimeter is a linear measurement, a uniform r% change in all dimensions produces the same r% change in perimeter.

Reverse percentage after an increase
Original perimeter = Final perimeter ÷ (1 + r/100)

Use this when the final perimeter is given after an r% increase.

Reverse percentage after a decrease
Original perimeter = Final perimeter ÷ (1 − r/100)

Use this when the final perimeter is given after an r% decrease.

Quick Tricks

Use the perimeter ratio for uniform scaling

If every side of a figure is multiplied by the same factor k, the perimeter is also multiplied by k. Therefore, the percentage change in perimeter equals the percentage change in each side length.

Example: If all sides increase by 20%, new perimeter = 1.2P, so the perimeter also increases by 20%.
Find the change before dividing

For a rectangle, calculate the old and new values of l + b. The factor 2 cancels when comparing the two perimeters.

Example: If l + b changes from 25 cm to 30 cm, the perimeter change is 2 × 5 = 10 cm, and the percentage change is 10 ÷ 50 × 100 = 20%.

Percentage Change in Perimeter Concepts

Direct calculation from two perimeter values

When the original and new perimeters are known, subtract the original value from the new value and divide by the original perimeter.

Use Percentage change = [(P₂ − P₁) ÷ P₁] × 100, where P₁ is the original perimeter and P₂ is the new perimeter. If P₂ is smaller than P₁, the result is negative and represents a decrease.

Example: A perimeter changes from 72 m to 90 m. Percentage change = (90 − 72) ÷ 72 × 100 = 18 ÷ 72 × 100 = 25% increase.

Effect of changing both rectangle dimensions

For a rectangle, calculate each perimeter using P = 2(l + b), then apply the percentage-change formula.

If the length changes from l₁ to l₂ and the breadth changes from b₁ to b₂, then the percentage change is [2(l₂ + b₂) − 2(l₁ + b₁)] ÷ [2(l₁ + b₁)] × 100. This simplifies to [(l₂ + b₂) − (l₁ + b₁)] ÷ (l₁ + b₁) × 100.

Example: For a rectangle changing from 12 cm × 8 cm to 15 cm × 9 cm, old perimeter = 40 cm and new perimeter = 48 cm. Percentage change = 8 ÷ 40 × 100 = 20%.

Uniform change in every side

If every side length changes by the same percentage, the perimeter changes by that same percentage.

If each side becomes (1 + r/100) times its original length, every term in the perimeter is multiplied by the same factor. Thus, a 15% increase in all side lengths gives a 15% increase in perimeter, and a 15% decrease gives a 15% decrease.

Example: A square has side 10 cm. If its side becomes 12 cm, the perimeter changes from 40 cm to 48 cm, which is a 20% increase.

Independent changes in rectangle dimensions

When the length and breadth change by different percentages, the perimeter change is not generally equal to either percentage.

Suppose the original dimensions are l and b. After changes of x% and y%, the new perimeter is 2[l(1 + x/100) + b(1 + y/100)]. The percentage change depends on the contribution of each dimension to the original sum l + b.

Example: For a 20 cm × 10 cm rectangle, increasing length by 10% and breadth by 20% gives new dimensions 22 cm and 12 cm. Old perimeter = 60 cm, new perimeter = 68 cm, so the increase is 8 ÷ 60 × 100 = 13⅓%.

Reverse percentage change

To recover an original perimeter, divide the final perimeter by the relevant multiplier rather than subtracting the percentage directly.

After an r% increase, divide by 1 + r/100. After an r% decrease, divide by 1 − r/100. Direct subtraction from the final value gives an incorrect result because the percentage is based on the original perimeter.

Example: If a final perimeter of 66 cm follows a 10% increase, the original perimeter is 66 ÷ 1.10 = 60 cm.

Percentage Change in Perimeter Visual Guide

Use the diagram or chart below to understand the concept clearly.

Perimeter of a rectangle

Visual guide: Perimeter of a rectangle
Length: l Breadth: b Perimeter: 2(l + b)
A rectangle with length l and breadth b has perimeter 2(l + b).

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Practice Percentage Change in Perimeter Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Quick Revision Notes

Percentage Change in Perimeter: Revision Points

Use these formulas and rules for quick calculation.

  • Percentage change = [(New perimeter − Original perimeter) ÷ Original perimeter] × 100.
  • Always use the original perimeter as the denominator.
  • For a rectangle, P = 2(l + b); for a square, P = 4a.
  • If all linear dimensions change by the same percentage, the perimeter changes by the same percentage.
  • For different changes in length and breadth, calculate both perimeters before finding the percentage change.
  • After an r% increase, Original = Final ÷ (1 + r/100).
  • After an r% decrease, Original = Final ÷ (1 − r/100).

Related Topic Explainers

Area of Square → Perimeter of Square → Area of Rectangle → Perimeter of Rectangle → Area of Triangle → Perimeter of Triangle → Heron's Formula → Area of Triangle Using Two Sides and Included Angle →

Percentage Change in Perimeter FAQs

What is the percentage change if the perimeter increases from 80 cm to 100 cm?

Percentage change = (100 − 80) ÷ 80 × 100 = 25% increase.

If every side of a polygon increases by 10%, what happens to its perimeter?

Its perimeter also increases by 10%, because perimeter is a linear measurement and every side is multiplied by 1.10.

A rectangle changes from 10 cm × 6 cm to 12 cm × 8 cm. What is the percentage change in perimeter?

Old perimeter = 32 cm and new perimeter = 40 cm. Percentage change = 8 ÷ 32 × 100 = 25% increase.

Can the percentage change in perimeter be found by adding the percentage changes in a rectangle’s length and breadth?

Not generally. The result depends on the original length and breadth. Calculate the old and new perimeters unless both dimensions change by the same percentage.

What is the original perimeter if it becomes 132 cm after a 10% increase?

Original perimeter = 132 ÷ 1.10 = 120 cm.

What is the original perimeter if it becomes 85 cm after a 15% decrease?

Original perimeter = 85 ÷ 0.85 = 100 cm.

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