GATE 2016 EC (EC2) – Question 10

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

A 340 mm wire is cut into two parts. One forms a square and the other a rectangle with side ratio 1:2. What square side length in mm minimizes their combined area?

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Correct answer: (B) 40

Explanation

Let the square side be x and the rectangle sides be y,2y. The wire constraint is 4x+6y=340, so $y=(340-4x)/6$.

Total area is $A=x^2+2y^2=x^2+(340-4x)^2/18$. Differentiate: $A\prime=2x-(4/9)(340-4x)$.

Setting it to zero gives 34x=1360, hence **x=40 mm, B**. The second derivative 34/9 is positive, confirming a minimum.

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