How to Tell If A Triangle Is Real?

Question

Our teacher gave supposedly gave us the lengths of each of the trangle's sides. How can I tell if it is a real triangle? I think there is a rule about the sides...


Thanks :)

Answer 1

For a triangle sum of any two sides should be greater than the 3rd side. You have to do only one check. take the sum of 2 lower sides and check against the 3rd one. If it is more then it is a triangle else no
if same then 3 points are collinear.

Answer 2

The three basics of a triangle are that it has three sides and the internal angles sum to 180 degrees and the sum of the two short sides cannot be shorter than the long side. Fit your dimensions and then measure the angles, if the lengths are impossible to connect then it is a bogus data set. There is another test, but it if for right-triangles only (one angle is 90 degrees): the sum of the square of the two sides is the square of the hypoteneus (the longest line that connects the other two which form the right angle, 90 degrees). If one side, say, is 3 and another side is, say, 4, and they are at a right angle, 90 degrees, then the line connecting the ends of those two sides should be 5 (9+16=25, square root of 25 is 5). If the two short sides of a triangle total less than the long side, then they cannot connect and it cannot be a triangle. If the two short sides sum at the same length to the long side, then you have two lengths laying on an equal total length and there is no triangle--your figure is a straight line. If the two short sides are of equal length, that is called an isosceles triangle. If you have three sides that are all the same length, that is an equalateral triangle.

Usually, if you have three elements you can define the rest of the triangle, two sides and an angle, a side and two angles, or three sides. With three angles you can establish a solution set in the form of an algebraic equation, but then you still need to plug in a length in order to determine the dimensions of the other two sides to see if it fits your set of angles. These things take more explanation and I've already given more than the 2-10 points are worth.

Answer 3

The triangle inequality says the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.

That means you cannot have a triangle with sides 2, 4 and 7, because 2+4 < 7.

In fact, for any real numbers X, Y and Z, if the sum of any two of the numbers is greater than the 3rd, then you can find a triangle with sides X, Y and Z.

Answer 4

The 'triangle inequality' states that c < a + b and c > |a - b| where a, b, and c are the lengths of the triangle. So you have to check whether or not the largest side is less than the sum of the 2 smaller sides.

If that's true then it turns out the smallest side is greater than the difference of the other 2 sides, so you don't have to check that.

Answer 5

Hi. You don't say if it is a right triangle or not but if so, "the square of the hypotenuse will be equal to the sum of the squares of the two adjacent sides" - Scarecrow in the Wizard of OZ

Answer 6

Agreeing with previous replies (I don't care about the points)... Are all 3 sides touching (connected) to make one line? If not, then it is not a triangle--or any shape--just 2 or 3 lines.

Answer 7

the sum of the short sides must be greater than the long side

Answer 8

sum of two sides must be greater than the third side.
Check out this problem
http://math-homeworkhelp.blogspot.com/2006/07/sides-of-triangle.html

Answer 9

Wacky idea-- cut lengths of paper in those lengths (or some smaller version with the same number of increments) and see if the three can fit.

Answer 10

three sides, three angles and the angles add up to 180 degrees