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GATE DA 2025 Q5: Rectangle: effect of increasing the width by 10%

Question

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

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Answer: C (official GATE 2025 final answer key)

Concept used: Percentage change in perimeter, diagonal and area when one dimension changes.

First step: Write the new area as L×1.1WL \times 1.1W and compare it with LWLW; then check whether the perimeter 2(L+1.1W)2(L + 1.1W) and diagonal L2+1.21W2\sqrt{L^2 + 1.21W^2} also grow by exactly 10%.

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Source: official GATE 2025 DA question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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