- #1
Ismael Nunez
- 12
- 0
Anyone want to take a crack at it? My class has been discussing it: Find the length of AB:http://t4.rbxcdn.com/84e25f3830d66e6bbaeaba48e35c0781
Is the Pythagorean Theorem Applied to Determine the Length of AB?
- Thread starter Ismael Nunez
- Start date
In summary, the conversation is discussing finding the length of side AB in a given image and the confusion surrounding the calculation. The final solution involves using the distance formula and simplifying the calculation by choosing appropriate axes. The final answer is 6.
- #2
Misha Kuznetsov
- 49
- 4
Six.
- #3
Ismael Nunez
- 12
- 0
Will you please elaborate?Misha Kuznetsov said:
- #4
Jerry Friedman
- 13
- 1
6?
- #5
Ismael Nunez
- 12
- 0
Ok, great, but how did you get there?Jerry Friedman said:
- #6
Ismael Nunez
- 12
- 0
I am probably wrong, but I got sqrt(34).
- #7
Jerry Friedman
- 13
- 1
Find the coordinates of point A and use the distance formula to get AB. There are pleasant cancellations.
- #8
Misha Kuznetsov
- 49
- 4
I just found the hypotenuse of a triangle with legs 4+sqrt(2) and 4-sqrt(2).
- #9
Ismael Nunez
- 12
- 0
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?Jerry Friedman said:
- #10
Misha Kuznetsov
- 49
- 4
No, each leg would be sqrt(2) .
- #11
Ismael Nunez
- 12
- 0
Alright, I see my mistake, I checked my work again. Thanks.Misha Kuznetsov said:
- #12
Misha Kuznetsov
- 49
- 4
Yep, no problem. 
- #13
Maths Absorber
- 59
- 3
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.
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.
- #14
epenguin
Homework Helper
Gold Member
- 3,636
- 1,010
Was it given that the figures with sides 2 and 4 are squares?
If so, 6.
If so, 6.
Last edited:
What is the Pythagorean Theorem?
The Pythagorean Theorem is a mathematical principle that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Who is credited with discovering the Pythagorean Theorem?
The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, although there is evidence that it was known and used by other civilizations prior to him.
How is the Pythagorean Theorem used in real life?
The Pythagorean Theorem has many practical applications, such as in construction, navigation, and engineering. It can be used to calculate distances, heights, and angles in various situations.
Can the Pythagorean Theorem be used in non-right triangles?
No, the Pythagorean Theorem only applies to right triangles, where one of the angles is a perfect 90 degrees.
What is the formula for the Pythagorean Theorem?
The formula for the Pythagorean Theorem is a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides (legs) of a right triangle, and c is the length of the hypotenuse.
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