Q&A for How to Determine if Three Side Lengths Are a Triangle

Then you have an equilateral triangle.

Yes. It's called an equilateral triangle, and it can work because two side lengths added together are bigger than the third side.

The resulting figure is not a triangle, because the two smaller sides must be on top of the larger side in order to connect to the larger segment's endpoints. This figure has no area, and is a line segment, not a triangle.

> means "is greater than." < means "is less than."

No. 4+6 is only 10, which is less than 11.

As stated above, as long as the sum of any two of those measurements is greater than the third measurement, the three "sides" will fit together to make a triangle. In the case of the three numbers you propose, they will form a triangle. If, for example, the 24 had been 18 instead, 7+18 would be less than 26, and those lengths could not form a closed figure.

Yes. Let a = 9, b= 9, and c = 1. a + b = 9 + 9 = 18. This is greater than c, which is 1. a + c = 9 + 1 = 10. This is greater than b, which is 9. b + c = 9 + 1 = 10. This is greater than a, which is 9.

You can use one of the trigonometric functions arcsin, arccos, or arctan, depending on which angle you are trying to find and which sides you are using.

The short answer is no. The longer answer is that you get what's called a degenerate triangle, which in this case amounts to nothing more than a straight line 12 units long. All the formulas and theorems you know for working with triangles still work. The law of cosines gives angles of 0, 0 and 180. Area formulas all give 0.

Assuming that's all the information you know, you could designate any of the sides as the base, but you'd need to know at least one of the angles adjacent to the base in order to determine the height.

No. Each side's length must be less than the sum of the other two sides' lengths. In this case 3 is not less than the sum of 1 plus 2.

If the sum of the two sides is greater than the third side. A+B greater than C. A+ C greater than B. B+C greater than A.

No. Let's say that a=6, b=10, and c=4. This cannot form a triangle because when you do a+b>c, you see that the triangle cannot be formed closed.

No, because the two smallest sides don’t add up to be longer than the largest. Think of it this way. The 6 unit side is trying to fit between sides exactly, but they can’t push them out far enough to work.

It is enough. Although a triangle satisfies all three versions of the inequality, two of them are obviously true, so it suffices to check only the remaining one.

No, it’s not. Add the two smallest lengths together (3 and 3) and you get 6, which is not greater than 7. Think of it this way. 7 is the hypotenuse, but it can’t connect the two sides because it’s too long and doesn’t reach exactly between them.

No, because each of those lengths is not greater than the sum of the other two lengths.

No. 12 + 3 = 15. Adding any two sides must always equal a number greater than the remaining side.

If the squares of two sides are greater than the square of the remaining side, the triangle is acute. (A^2 + B^2 > C^2.) If the squares of two sides are equal to the square of the remaining side, the triangle is right. (A^2+B^2 = C^2.) If the squares of two sides are less than the square of the remaining side, the triangle is obtuse. (A^2+B^2

If the sum of the lengths of any two straight lines is greater than the length of a third straight line, the three lines can form a triangle.

No, lines of those lengths will not form a triangle, because 5 + 4 is less than 11.

If it's a convex quadrilateral (with no obtuse angles), it has 360 degrees.

No, because 10 is not less than the sum of 7 and 2.

If it's a right triangle, you can use the Pythagorean Theorem where a² + b² = c ². In this formula, a and b are the legs, and c is the hypotenuse--or the longest side. If the triangle is not a right triangle, the process of finding the third side is more difficult and involves knowing the angles and applying trigonometry.

Yes.

As long as the sum of the length of any two sides is greater than the remaining side, you can form a triangle.

Yes, because each of those lengths is shorter than the sum of the other two lengths.

The remaining side could be anywhere between 0 and 10. Unless you have the angles for the two sides you already have, you can't determine the length of the third side.

You would also have to know at least two of the interior angles.

First evaluate the square root(s). For example, √2 = 1.414). Then proceed as usual.