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

Quantitative Aptitude (CDS) Mensuration 2D

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√2 cm²

24√3 cm²

48√3 cm²

64√3 cm²

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Explanation:

Let the side of each square be x cm and the side of each equilateral triangle be y cm.
Length of diagonal of square
=√2x=12√2⇒x=12cm
Perimeter of square = Perimeter of equilateral triangle
∴4x=3y
⇒3y=4×12
⇒y=16cm
Therefore, area of equilateral triangle=√3/4 ×(16)2=64√3 cm2