Question

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). Pleas

Answer 1

this is really hard and i need helpp

Answer 2

the height in this first isosceles triangle will be sqrt(sqrt5 squared - 1)=sqrt4=2
so if the height is 2 so than area of this isosceles triangle will be =2*(1*2/2)=2

Answer 3

im still lost....

Answer 4

chelseaboo61 look how you will can get this four (4) little triangles from what you can makeing this squart with area equal 2
- so if you write tha midle point on the height line of the first isosceles triangle and unite this point by one line parallel with the base of this isosceles triangle with those two sides of the isosceles triangle and so you will get one little triangle

Answer 5

ohhh ok lol i was lost... but i kinda get it noww

Answer 6

i am lost a little too, but i can get the square root of two in the picture.
\[AB=AC=\sqrt{5}\]\[AD=DC=1,AD=2\] so if M is the midpoint of the height then
\[MD=1\] and so \[AMB=MC=\sqrt{2}\] and so
\[BMC\] is half of the square

Answer 7

i meant
\[BM=MC=\sqrt{2}\] so one triangle takes up half the square with both sides
\[\sqrt{2}\] and diagonal 2
i am still trying to get the rest. maybe jhonny9 has it

Answer 8

@jhonny9 can you draw a picture or alter mine so i can see what triangles you have?

Answer 9

but are the triangles congruent??

Answer 10

after you need parte the base of the first isosceles triangle in 2 equales partes so after this you need unit those points so that you will get down the first line 3 equales ,the same little triangles like the first little and hence if you arrange in one square those all little 4 triangle you will get the needed,necessary square what will have area equal with area of this isosceles triangle

Answer 11

yes those all 4 little triangles will be congruents

Answer 12

ok thanks soooooooo much i finally figured it out :)

Answer 13

@chelseboo please draw it so i can see!

Answer 14

chelseaboo61 you have figured how i have wrote to you ?
so than i think that was very easy
yes ???

Answer 15

picture?

Answer 16

yess i got it now. i just wasnt understanding the 4 little triangles

Answer 17

but at finaly is understood it ?

Answer 18

picture?????