Question
An equilateral triangle is described on the diagonal of a square . What is the ratio of the area of the triangle to that of the square ?
Answer: Option C
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Let the side of the square be a cm.
Then, the length of its diagonal = `sqrt(2)` a cm.
Area of equilateral triangle with side `sqrt(2)`a = `sqrt(3)/4 xx (sqrt(2)a)^2` = `(sqrt(3) a^2)/(2)`
`:.` Required ratio = `(sqrt(3)a^2)/(2) : a^2` = `sqrt(3)` : 2
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