GATE 2026 AR — Architecture – Question 27

Design and Graphics · Ergonomics, Ratio and proportion, Scales in design, Organization of space · 1 mark · Numerical answer

Starting with square ABCD of side 1 cm, the figure develops successive golden-mean rectangles. Find length IJ in cm, to three decimals.

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Correct answer: 2.600 to 2.650

Explanation

Let φ=(1+√5)/2≈1.618034. The first golden rectangle has long sideφ when its short side is 1. Continuing the similar construction gives the next long sideφ²=φ+1=2.618034. Thus IJ=2.618 cm. The second construction multiplies both corresponding dimensions byφ.

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