SOLUTION: A square is inscribed fully inside an equilateral triangle. The triangle has a side length of 10. The square shares one side with a triangle side (but the square side is shorter th

Algebra ->  Triangles -> SOLUTION: A square is inscribed fully inside an equilateral triangle. The triangle has a side length of 10. The square shares one side with a triangle side (but the square side is shorter th      Log On


   

Question 844584: A square is inscribed fully inside an equilateral triangle. The triangle has a side length of 10. The square shares one side with a triangle side (but the square side is shorter than the triangle side. The square's other two vertices each touch another side of the triangle.
I already know the entire triangle has an area of 25 radical 3. I would like to find the area of the square. Or the area of the triangle excluding the square.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
see http://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.262990.html
t=10
s=side of square
t/s=2.155
2.155s=t
s=t/2.155
s-10/2.155=4.64
4.64^2=21.53
also
http://gmatclub.com/forum/an-equilateral-triangle-has-a-square-inscribed-in-it-side-139965.html