45-45-90 Triangle Question

[Alpha Centauri]

Hey guys. Can someone explain where they get the equation side = 2 / root 2? I understand there is a 45 45 90 triangle and that the hypotenuse of it is 2, so therfore there is some relationship with the hypotenus equaling x root 2, because the other sides are simply X's since it is a special triangle. Thanks

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[DMikes]

Hey guys. Can someone explain where they get the equation side = 2 / root 2? I understand there is a 45 45 90 triangle and that the hypotenuse of it is 2, so therfore there is some relationship with the hypotenus equaling x root 2, because the other sides are simply X's since it is a special triangle. Thanks

I presume you're simply looking for the area of the square and you are only given that the diameter of the circle is = 2. You know that the circle circumscribes the square and thus the hypotenuse = the diameter.
You also know the relationship between the isosceles triangle is 1, 1, sqrt(2).

You need to find the side length. So, because you know that diameter = 2 and that hypotenuse of that special triangle = sqrt(2), you can easily calculate the side length by simply finding the proportion. which would be 2/sqrt(2).

then you square that to get the area. if you need more explanation let me know. Not sure if that was helpful.

 

[Alpha Centauri]

I presume you're simply looking for the area of the square and you are only given that the diameter of the circle is = 2. You know that the circle circumscribes the square and thus the hypotenuse = the diameter.
You also know the relationship between the isosceles triangle is 1, 1, sqrt(2).

You need to find the side length. So, because you know that diameter = 2 and that hypotenuse of that special triangle = sqrt(2), you can easily calculate the side length by simply finding the proportion. which would be 2/sqrt(2).

then you square that to get the area. if you need more explanation let me know. Not sure if that was helpful.

Can you just explain the part where you made the proportion 2 / sqrt 2 and where those numbers are coming from (which sides of the triangles)

 

[DMikes]

Can you just explain the part where you made the proportion 2 / sqrt 2 and where those numbers are coming from (which sides of the triangles)

One sec. I'll draw it out

Edit: pic

 

[DMikes]

Hopefully that makes sense!

 

[Alpha Centauri]

Hopefully that makes sense!

Omg thank you so much! I was about to rip my hair out. I completely understand it now, it was just converting from the standard 45 45 90 triangle to the triangle we have with the new side measurements

 

[DMikes]

Omg thank you so much! I was about to rip my hair out. I completely understand it now, it was just converting from the standard 45 45 90 triangle to the triangle we have with the new side measurements

Exactly! No problem