1.5m
Plug the side lengths into the Pythagorean theorem in place of a and b. If a2 + b2 = c2, it's a right triangle. C needs to be an integer, so c2 will be a perfect square.
Those ones, there!
There cannot be an integral set of values. The lengths need to be in the ratio 1 : sqrt(3) : 2.
It is a trapezoid that has one set of opposite parallel lines of different lengths.
1.5m
Plug the side lengths into the Pythagorean theorem in place of a and b. If a2 + b2 = c2, it's a right triangle. C needs to be an integer, so c2 will be a perfect square.
Those ones, there!
No because the given sides do not comply with Pythagoras' theorem for a right angle triangle.
Infinitely many. The smallest side of a triangle can have infinitely many possible lengths.
There are many lengths that can be used to make triangles. Basically take the longest side, add the two shorter sides together, it can be a triangle as long as the 2 shorter sides added together are longer than the longest side.
If any of its 2 sides is not greater than its third in length then a triangle can't be formed.
3, 4 and 5 units of length
They are Pythagorean triples
There are lots of sets of numbers that fit that definition! But the important thing to remember about triangles is the Third Side Rule, or the Triangle Inequality, which states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides. So you can have a triangle with sides of 3, 4 and 5 because 3 < 4 + 5, 4 < 3 + 5 and 5 < 3 + 4; and because 3 > 5 - 4, 4 > 5 - 3 and 5 > 4 - 3. But you can't have a triangle with sides 1, 2 and 8, for example. Just imagine three pieces of wood or three straws with lengths 1, 2 and 8. Put the longest piece, 8, horizontally on the table. Then put the other two, one at each end of the longest piece. Could those two shorter sides ever meet to form a triangle? No, never!-----------------------------------------------------------------------------------------------------------The length is always positive, so that all real positive numbers can represent the length of sides of a triangle: {x| x > 0}.------------------------------------------------------------------------------------------------------------Whoever added that to my answer, sorry, I beg to differ! The question asked what SET of numbers cannot represent the lengths of the sides of a triangle. There are infinite possibilities for that. While the lengths are always a set of real positive numbers, not every possible set of real positive numbers is a potential set of numbers that represent the lengths of the sides of a triangle!
Multiples of 3, 4, 5 because 32 + 42 = 52 for example sides can be 6, 8, 10 or 15, 20, 25 or 9, 12, 15 etc. of course the largest number of each set will be the hypotenuse.
There cannot be an integral set of values. The lengths need to be in the ratio 1 : sqrt(3) : 2.