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GATE 2016 ME (ME3) – Question 10

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?

  1. 30
  2. 40
  3. 120
  4. 180

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Show answer and explanation

Correct answer: (B) 40

Explanation

Let square side be a and rectangle sides b,2b. Then4a+6b=340 and A=a²+2b²=a²+(340−4a)²/18. Setting A′=2a−(4/9)(340−4a)=0 gives34a=1360, hence **a=40m, B**. A″=34/9>0 confirms a minimum.