If the side = 10 is ab, 6 is ac and 3 is bc, then as angles a an b approach zero, the triangle approaches 2 straight lines. If ab < ac + bc, then it is a triangle. If ab = ac + bc, it is not a triangle, rather 2 lines drawn over each other. Not sure about this, but seem correct (and I stand to be corrected), if ab is the diameter of a circle, then the angle c must be 90 deg, as that would be the smallest "real" triangle that could exist within a circle (as pythagorean) and 10sq does not equal 6sq + 3sq.
It violates the triangle inequality: the length of any side of a given triangle is greater than or equal to the difference of the other two sides. It is not the case that 3 >= 10 - 6; therefore, the triangle inequality doesn't hold. ◼
This is because there is a theorem that states that the sun of any two sides of a triangle should always be greater than its third which isn't possible as 3+6 is 9 which is less than 10
It's simple common sense. Imagine that you have a 10' board and a 9' board. If you cut the 9' board into two pieces, regardless of the lengths of those pieces, you'll never be able to make a triangle from the resulting three pieces because the two shorter pieces are too short.
I always remembered the saying from my 7th grade algebra teacher. it times itself plus it times itself square rooted. A-squared plus B- squared then square root that number to find C so 3×3 is 9 and 4×4 is 16 . 9+16 IS 25. The square root of 25 is 5. So I guess im old school 😮
If the side = 10 is ab, 6 is ac and 3 is bc, then as angles a an b approach zero, the triangle approaches 2 straight lines. If ab < ac + bc, then it is a triangle. If ab = ac + bc, it is not a triangle, rather 2 lines drawn over each other. Not sure about this, but seem correct (and I stand to be corrected), if ab is the diameter of a circle, then the angle c must be 90 deg, as that would be the smallest "real" triangle that could exist within a circle (as pythagorean) and 10sq does not equal 6sq + 3sq.
My guess is that the longest side cannot be longer than the combination of the two shorter sides.
If the 3-side and the 6-side are laid flat = straight line it would total 9. The remaining side = 10-line couldn't end at 9..
It violates the triangle inequality: the length of any side of a given triangle is greater than or equal to the difference of the other two sides.
It is not the case that 3 >= 10 - 6; therefore, the triangle inequality doesn't hold. ◼
Because the short sides (the opposite and the adjacent) combined are shorter than the long side (the hypotenuse).
This is because there is a theorem that states that the sun of any two sides of a triangle should always be greater than its third which isn't possible as 3+6 is 9 which is less than 10
Great review.
don't remember this theorem but it makes sense....
Euclidan Geometry ?
It's simple common sense. Imagine that you have a 10' board and a 9' board. If you cut the 9' board into two pieces, regardless of the lengths of those pieces, you'll never be able to make a triangle from the resulting three pieces because the two shorter pieces are too short.
With this triangle, walking the side length 6 and the side length 3 would be the shortcut instead of cutting across.
I always remembered the saying from my 7th grade algebra teacher. it times itself plus it times itself square rooted. A-squared plus B- squared then square root that number to find C so 3×3 is 9 and 4×4 is 16 . 9+16 IS 25. The square root of 25 is 5. So I guess im old school 😮
I’ve never heard about that rule for triangles. We didn’t study that in geometry
Simple. 6^2 + 3^2 = 45. So the long side is root(45).
Rule (A+B) > C
The rule is simple: both catheus sum must be bigger than hypotenuse length to be able to create this kind of triangle
A(2) +b(2) =C(2)
Sum of any two sides must exceed length of third. Not the case here.
This one was really a one second answer. Just rotate the 3 side in line with the 6 side and you have a length of max 9...
If two sides are three and six the third side needs to be greater than 6-3 and less than 6+3.
Apologies, but you never defined "natural triangle", nor stated why "triangle inequality" does not make one, nor why we should care.
Ok, paused at the beginning as usual.
6+3=9 which isn't long enough to reach the hypotenuse which is 10.
Because 10 > 3 + 6. In a degenerate triangle, where the angle between the 3 and the 6 sides is 180 degrees, the third side is still only 9.
Pythagoras asqu×bsqu=csqu
Only for right triangles
only for right triangles
Because 6 + 3 = 9 and the third side is 10 so they wouldn't meet
😇👍
Long winded you only needed about two min.
Waste of ten minutes for anyone with an ounce of common sense
Obviously he's teaching the other 99% of the population.
It would have to be a 3, 4, 5 or multiples thereof!