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If the two regions, an equilateral triangle with side t and [#permalink]
09 Apr 2008, 22:44

If the two regions, an equilateral triangle with side t and square with side s, have the same area, what is the ratio t:s? A. 2:3 B. 16:3 C. 4:sqrt(3) D. 2:sqrt(3)^4 E. 4:sqrt(3)^4

This the way I solved the question:

The area of the triangle can be calculated as height*base*1/2 (30-60-90 >> X : X*sqrt(3) : 2X >> t/2 : t*sqrt(3)/2 : t ) Height = sqrt(3)t/2 Base = t Area = sqrt(3)*t^2/4

The area of square is s^2 sqrt(3)*t^2/4 = s^2 >> s = 3*t/2

The ratio: t/s = t/(3*t/2)

Completely blind here: what did I do wrong?? Please, point my mistake... Thank you

If the two regions, an equilateral triangle with side t and square with side s, have the same area, what is the ratio t:s? A. 2:3 B. 16:3 C. 4:sqrt(3) D. 2:sqrt(3)^4 E. 4:sqrt(3)^4

This the way I solved the question:

The area of the triangle can be calculated as height*base*1/2 (30-60-90 >> X : X*sqrt(3) : 2X >> t/2 : t*sqrt(3)/2 : t ) Height = sqrt(3)t/2 Base = t Area = sqrt(3)*t^2/4

If the two regions, an equilateral triangle with side t and square with side s, have the same area, what is the ratio t:s? A. 2:3 B. 16:3 C. 4:sqrt(3) D. 2:sqrt(3)^4 E. 4:sqrt(3)^4

This the way I solved the question:

The area of the triangle can be calculated as height*base*1/2 (30-60-90 >> X : X*sqrt(3) : 2X >> t/2 : t*sqrt(3)/2 : t ) Height = sqrt(3)t/2 Base = t Area = sqrt(3)*t^2/4

Well, we are given equilateral triangle 60 - 60 - 60 A height bisects the angle of the equilateral triangle. Therefore, when we draw a height we will get 2 similar triangles: 30-60-90 and 30-60-90.

If the two regions, an equilateral triangle with side t and square with side s, have the same area, what is the ratio t:s? A. 2:3 B. 16:3 C. 4:sqrt(3) D. 2:sqrt(3)^4 E. 4:sqrt(3)^4

This the way I solved the question:

The area of the triangle can be calculated as height*base*1/2 (30-60-90 >> X : X*sqrt(3) : 2X >> t/2 : t*sqrt(3)/2 : t ) Height = sqrt(3)t/2 Base = t Area = sqrt(3)*t^2/4

The area of square is s^2 sqrt(3)*t^2/4 = s^2 >> s = 3*t/2

The ratio: t/s = t/(3*t/2)

Completely blind here: what did I do wrong?? Please, point my mistake... Thank you

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