How to Dissect an Isosceles Triangle into 4 Triangles for a Square

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SUMMARY

The discussion focuses on dissecting an isosceles triangle with legs measuring sqrt(5) and a base of 2 into four triangles that can be arranged to form a square. The area of the isosceles triangle is equal to the area of the square, leading to the conclusion that the side length of the square must be sqrt(2). Participants emphasize the necessity of cutting the legs of the triangle to fit within the dimensions of the square, as sqrt(5) exceeds the square's side length.

PREREQUISITES
  • Understanding of isosceles triangle properties
  • Basic knowledge of geometric dissection
  • Familiarity with area calculations for triangles and squares
  • Concept of arranging geometric shapes
NEXT STEPS
  • Explore geometric dissection techniques
  • Learn about the properties of isosceles triangles
  • Study area formulas for various geometric shapes
  • Investigate practical applications of geometric arrangements
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Mathematicians, geometry enthusiasts, educators, and students tackling geometric dissection problems.

gravenewworld
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I've been stuck on this problem for over 2 hrs. The problem is that I have an isosceles triangle with legs measuring sqrt(5) each and the base measuring 2. I have to find a way to dissect the isosceles triangle into 4 triangles so that the 4 triangles can be arranged into a square. So far I know that obviously the side of the square has to be sqrt(2) since area iso triangle=area square=side of square^2. I also know that the legs of the isoceles triangle must be cut some how because there is no way a length of sqrt(5) will fit into a square with dimensions of sqrt(2)xsqrt(2). Please any hints or help would be vastly appreciated.
 
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That's a good one! Hmm...!
 
gravenewworld said:
I've been stuck on this problem for over 2 hrs. The problem is that I have an isosceles triangle with legs measuring sqrt(5) each and the base measuring 2. I have to find a way to dissect the isosceles triangle into 4 triangles so that the 4 triangles can be arranged into a square. So far I know that obviously the side of the square has to be sqrt(2) since area iso triangle=area square=side of square^2. .


Nice problem. It is against our principles, but I must show the solution. I just can't help . :smile:

ehild
 
Last edited:

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