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

AI Thread Summary
An isosceles triangle with legs measuring sqrt(5) and a base of 2 needs to be dissected into four triangles that can form a square. The area of the triangle is equal to the area of the square, leading to the conclusion that the side length of the square must be sqrt(2). The challenge lies in cutting the legs of the triangle appropriately, as their length exceeds the dimensions of the square. Assistance is sought to find a method for this dissection. The problem presents an intriguing geometric challenge.
gravenewworld
Messages
1,128
Reaction score
27
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.
 
Physics news on Phys.org
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:

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

I Geometry problem of interest with a 3-4-5 triangle
2
Replies
59
Views
2K
Perimeter relationships -- Dividing a rectangle into 4 triangles
Replies
2
Views
3K
Solving an Electric Field Problem in Equilateral Triangle Geometry
Replies
5
Views
6K
What is the area of a square drawn inside a triangle?
Replies
8
Views
2K
MHB Find the height and base of a trapezium
Replies
1
Views
2K
MHB What is the area of an isosceles triangle with side lengths 6, 6, and 4?
Replies
1
Views
2K
Isosceles triangle in information theory
Replies
4
Views
2K
MHB Why Can't a Right Triangle Have Sides that Add Up to the Area of Squares?
Replies
2
Views
2K
Isosceles Triangles with Congruent Lateral Sides
Replies
5
Views
3K
Photo Contest - Isosceles Triangle (6/20-6/26)
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top