An equilateral triangle and a square are constructed using metallic wires of equal length What is th...........

Quantitative Aptitude (CDS) Mensuration 2D

An equilateral triangle and a square are constructed using metallic wires of equal length. What is the ratio of area of triangle to that of square?

3:4

2:3

$4\sqrt{3}:9$

$2\sqrt{3}:9$

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Explanation:

let a_tbe one side of triangle and a_s be one side of square.
Now according to question 3a_t = 4a_s
a_t=(4/3)a_s
a_t² = 16/9 a_s²
$=> \frac{Area \: of \: triangle}{Area \: of \: square}=\frac{\frac{\sqrt{3}}{4}at^{2}}{a_{s}^{2}}$
Substituting value of a_t²above , we get
$=> \frac{Area \: of \: triangle}{Area \: of \: square}=\frac{\sqrt{3}}{4}\times \frac{9}{16}$
$=\frac{4\sqrt{3}}{9}$