Is the Pythagorean Theorem Applied to Determine the Length of AB?

[Ismael Nunez]

Anyone want to take a crack at it? My class has been discussing it: Find the length of AB:http://t4.rbxcdn.com/84e25f3830d66e6bbaeaba48e35c0781

 

[Misha Kuznetsov]

Six.

 

[Ismael Nunez]

Six.

Will you please elaborate?

 

[Jerry Friedman]

6?

 

[Ismael Nunez]

6?

Ok, great, but how did you get there?

 

[Ismael Nunez]

I am probably wrong, but I got sqrt(34).

 

[Jerry Friedman]

Find the coordinates of point A and use the distance formula to get AB. There are pleasant cancellations.

 

[Misha Kuznetsov]

I just found the hypotenuse of a triangle with legs 4+sqrt(2) and 4-sqrt(2).

 

[Ismael Nunez]

Find the coordinates of point A and use the distance formula to get AB. There are pleasant cancellations.

I did, and I still got sqrt(34)... One question though, the square at the top left corner... If split vertically, to get 4 triangles, wouldn't the legs of one of those triangles be one?

 

[Misha Kuznetsov]

No, each leg would be sqrt(2) .

 

[Ismael Nunez]

No, each leg would be sqrt(2) .

Alright, I see my mistake, I checked my work again. Thanks.

 

[Misha Kuznetsov]

Yep, no problem.

 

[Maths Absorber]

First, we choose the axes so as to simplify our calculation. Let us drop a perpendicular from A to the base and consider the the y-axis.

The location of A is (0, 4 +√²) and B is (4 - √2, 0)
Distance is √x²+y²

As we know, (a - b)² + (a + b)² = 2( a² + b²)

Which here is 2( 16 +2) = 36, the square root of it is 6.

I'm sorry if I skipped some steps. It's very difficult to type in mathematical notation.

 

[epenguin]

Was it given that the figures with sides 2 and 4 are squares?

If so, 6.