What will be the percentage increase in the area of a rectangle if each of its sides is increased by 25%?

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

When each side of a rectangle is increased by 25%, the new length is 1.25 times the original length, and the new breadth is 1.25 times the original breadth.
The new area becomes (1.25 × Length) × (1.25 × Breadth), which equals 1.5625 × (Length × Breadth).
An area factor of 1.5625 means the new area is 156.25% of the original area.
The percentage increase is the new percentage minus the original 100%, so 156.25% - 100% = 56.25%.
Alternatively, using the successive percentage change formula (x + y + xy/100), the calculation is 25 + 25 + (25 × 25)/100 = 50 + 6.25 = 56.25%.

Option A: This is an incorrect calculation and does not result from any standard formula related to area increase.
Option C: This is an incorrect calculation. It might arise from a misunderstanding of how percentage increases compound.
Option D: This is a common error made by simply adding the two percentage increases (25% + 25%). This is incorrect because it ignores the compound effect where the increase in one dimension also applies to the increase in the other dimension.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating percentage increase in the area of a geometric shape after a uniform percentage increase in its dimensions as background academic context rather than a clinical decision trigger.
This question tests basic quantitative aptitude, which is a component of the General Intelligence or Numerical Ability section in many nursing and other competitive examinations.
While not a direct clinical skill, strong numerical reasoning is foundational for nurses in tasks like medication dosage calculation, titrating IV drips, and interpreting changes in patient data over time.
What if? If the length was increased by 25% but the breadth was decreased by 25%, the net change would be 25 - 25 + (25 × -25)/100 = 0 - 6.25 = -6.25%, representing a 6.25% decrease in area.

How to Approach the Question

First, identify that the question asks for the percentage increase in the area, not the new area itself.
Recall the formula for the area of a rectangle: Area = Length × Breadth.
Represent the 25% increase in each side mathematically. A 25% increase is equivalent to multiplying the original value by 1.25.
Calculate the new area by multiplying the new length (1.25 × L) by the new breadth (1.25 × B).
Determine the factor by which the area increased (1.25 × 1.25 = 1.5625). This means the new area is 156.25% of the old area.
Subtract the original 100% to find the percentage increase: 156.25% - 100% = 56.25%.

Concept Tested & Keywords

Concept Tested: Calculating percentage increase in the area of a geometric shape after a uniform percentage increase in its dimensions.
Stem keywords: percentage increase, area of a rectangle, sides increased
Lead-in keywords: What will be

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