A square and an equilateral triangle have equal perimeter If the diagonal of the square is 12 2 cm t...........

Quantitative Aptitude (CDS) Coordinate Geometry

A square and an equilateral triangle have equal perimeter. If the diagonal of the square is 12 2 cm, then the area of the triangle is

$24\sqrt{2}\: cm^{2}$

$24\sqrt{3}\: cm^{2}$

$48\sqrt{3}\: cm^{2}$

$64\sqrt{3}\: cm^{2}$

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Explanation:

Diagonal of square = $12\sqrt{2}\: cm$

Side of square
$=\frac{12\sqrt{2}}{\sqrt{2}}\: cm$
Perimeter of square = 4 × 12 = 48 cm
Perimeter of equilateral triangle = 48 cm
Side of the equilateral triangle = 48/3 cm
= 16cm
$Area\: of\: triangle=\frac{\sqrt{3}}{4}a^{2}\: (where\: 'a'\: is\: any\: side\: of\: the\: triangle.)$
$= 64\sqrt{3}\: cm^{2}$