GATE 2022 AR — Architecture – Question 8

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

An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters of the equilateral triangle to square to circle?

$3\sqrt{3} : 2 : \sqrt{\pi}$
$\sqrt{3\sqrt{3}} : 2 : \sqrt{\pi}$
$\sqrt{3\sqrt{3}} : 4 : 2\sqrt{\pi}$
$\sqrt{3\sqrt{3}} : 2 : 2\sqrt{\pi}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) $\sqrt{3\sqrt{3}} : 2 : \sqrt{\pi}$

Explanation

Let the common area be $A$. Triangle: $\frac{\sqrt{3}}{4}a^2 = A$, so the perimeter is $3a = 2\sqrt{3\sqrt{3}}\sqrt{A}$. Square: perimeter $4\sqrt{A}$. Circle: $2\pi r = 2\sqrt{\pi}\sqrt{A}$. Dividing by $2\sqrt{A}$, the ratio is $\sqrt{3\sqrt{3}} : 2 : \sqrt{\pi}$.

More Quantitative Aptitude: Algebra, Geometry and Mensuration questions

GATE 2022 AR — Planning Q7 – A rhombus is formed by joining the midpoints of the sides of a unit square. What is the…
GATE 2022 AR — Planning Q8 – An equilateral triangle, a square and a circle have equal areas. What is the ratio of the…
GATE 2021 MN Q3 – Two fair six-faced dice numbered 1–6 are rolled independently. Find the probability of an…
GATE 2021 MN Q4 – Define p q=p-q and p q=pq. Evaluate (9(67))(7(65)).
GATE 2021 MN Q6 – From O, travel 3 units east and 4 south to P. Move northeast until reaching a point 6…
GATE 2021 MN Q9 – In square PQRS of side r, the shaded lens is the overlap of quarter-circles of radius r…

All Quantitative Aptitude: Algebra, Geometry and Mensuration questions →