GATE 2021 AR – Question 10

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

In an equilateral triangle, the sides are divided into 4, 6 and 8 equal parts respectively, each part having integer length in cm. Find the minimum triangle area in cm².

18
24
$48\sqrt3$
$144\sqrt3$

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Correct answer: (D) $144\sqrt3$

Explanation

The common side length must be divisible by 4, 6 and 8. Its least possible value is lcm(4, 6, 8)=24 cm. Equilateral area is $\sqrt3a^2/4=\sqrt3(24^2)/4=\mathbf{144\sqrt3}$ cm², **D**.

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