Question
A square and an equilateral triangle have equal perimeters . If the diagonal of the square is `12sqrt(2) cm^2`, then the area of the triangle is :
Answer: Option D
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Let the side of the square be a cm.
Then its diagonal = `sqrt(2) a cm`
Now , `sqrt(2) a = 12sqrt(2)`
`rArr a = 12 cm`
perimeter of the square = 4a = 48 cm. perimeter of the equilateral triangle = 48 cm.
Each side of the triangle = 16 cm .
Area of the triangle = `(sqrt(3)/4 xx 16 xx 16)cm^2 = (64sqrt(3)) cm^2`
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