GATE 2025 CY – Question 5

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

A rectangle has a length $L$ and a width $W$, where $L > W$. If the width, $W$, is increased by 10%, which one of the following statements is correct for all values of $L$ and $W$?

Perimeter increases by 10%.
Length of the diagonals increases by 10%.
Area increases by 10%.
The rectangle becomes a square.

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Correct answer: (C) Area increases by 10%.

Explanation

Let the new width be $W^\prime=1.1\,W$ (an increase of 10%), with $L$ unchanged.

**Area:** $A^\prime=L\times1.1W=1.1\,LW$. This is exactly **10% more**, for every $L$ and $W$. ✓
**Perimeter:** from $2(L+W)$ to $2(L+1.1W)$. The increase is $\dfrac{0.2W}{2(L+W)}=\dfrac{0.1W}{L+W}$ of the old perimeter, which is less than 10%, so it is not 10%. ✗
**Diagonal:** from $\sqrt{L^2+W^2}$ to $\sqrt{L^2+1.21W^2}$. The relative increase is less than 10%. ✗
**Becomes a square:** only if $L=1.1W$, which is not true for all $L$ and $W$. ✗

Answer **Area increases by 10%** (C).