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GATE 2025 DA – 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 $W$?

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

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Show answer and explanation

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

Explanation

The new area is $L \times 1.1W = 1.1LW$, which is exactly 10 % more, for every $L$ and $W$. The perimeter goes from $2(L + W)$ to $2(L + 1.1W)$, an increase of $\frac{0.1W}{L + W} < 10\%$. The diagonal $\sqrt{L^2 + W^2}$ grows by less than 10 % too. The rectangle becomes a square only if $L = 1.1W$, which is not true for all values.