Demostrate how Pythagoras came up with his theory, using a right angle triangle with side measurements of: a= 5cm and b= 4cm. Explain your thinking.
Need to draw it but can not, going to look for drawing.
Here it is :) The square with the triangles outside.
http//www.mathsisfun.com/geometry/pythagorean-theorem-proof.html
http//www.mathsisfun.com/geometry/pythagorean-theorem-proof.html
Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To demonstrate how Pythagoras came up with this theory, let's use the given right-angled triangle with side measurements of a = 5cm and b = 4cm.
1. First, let's label the sides of the triangle. The longer side, opposite the right angle, is called the hypotenuse and is denoted by c. The other two sides are the perpendicular side (a) and the base side (b), as shown:
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| /
| / a (5cm)
| /
| /
/
/
- b (4cm)
2. According to Pythagoras' theorem, we have the equation:
c^2 = a^2 + b^2
3. Substitute the given values into the equation:
c^2 = 5^2 + 4^2
4. Simplify the equation:
c^2 = 25 + 16
5. Add the values on the right side:
c^2 = 41
6. Now, to find the value of c, we need to take the square root of both sides:
c = sqrt(41)
7. Using a calculator, we can find that the square root of 41 is approximately 6.4.
So, for a right-angled triangle with side measurements of a = 5cm and b = 4cm, the length of the hypotenuse (c) is approximately 6.4cm.
Pythagoras came up with this theory by observing and analyzing various right-angled triangles and recognizing the relationship between the lengths of their sides. He then formulated the theorem based on this observation, which has been proven to hold true for all right-angled triangles.