1. Quote of the month: "Behind every great man is a woman rolling her eyes" - Jim Carrey
2. New quiz AQQ298 about an interlaced square and triangle puzzle:
An equilateral triangle (in red) and a square( in green) of side c are mutually inscribed one to each other.
Questions:
Good luck, and try to be among the first ones (i.e. goodies!)
Kuo-Chang
Great! It's time to publish the official (and right) answers!
The area of any triangle is obtained by (B x H)/2 where B is its base and H
its height.
It can be observed : B = x + c and c = x*tg(π/3) = x*√3 or x = c/√3
B = c*(1+1/√3)
H =(B/2) * tg(π/3) = (B/2) * √3 = (c/2)*(1+1/√3)* √3 = (c/2)*(1+√3)
Triangle area = ½ * c*(1+1/√3) * (c/2)*(1+√3) = 1.077 c²
Triangle is bigger than the square!
Congratulations to all having found the solutions and big applause to our 4 first winners:
steve12 , Sriramg , botha and MikeLh !
Also, most of you have noticed awards (i.e. goodies and acknowledgement have been distributed to the frequent winners! If you think you have been forgotten, please contact me.
Having that said, be ready for the next quiz!
Great! It's time to publish the official (and right) answers!
The area of any triangle is obtained by (B x H)/2 where B is its base and H
its height.
It can be observed : B = x + c and c = x*tg(π/3) = x*√3 or x = c/√3
B = c*(1+1/√3)
H =(B/2) * tg(π/3) = (B/2) * √3 = (c/2)*(1+1/√3)* √3 = (c/2)*(1+√3)
Triangle area = ½ * c*(1+1/√3) * (c/2)*(1+√3) = 1.077 c²
Triangle is bigger than the square!
Congratulations to all having found the solutions and big applause to our 4 first winners:
steve12 , Sriramg , botha and MikeLh !
Also, most of you have noticed awards (i.e. goodies and acknowledgement have been distributed to the frequent winners! If you think you have been forgotten, please contact me.
Having that said, be ready for the next quiz!
