Question

Try to construct triangles using match sticks. Some are shown here. Can you make a triangle with matchsticks?
(Remember you have to use all the available matchsticks.) Name the type of the triangle. If you cannot make a triangle, think of reasons for it.

Answer 1

Hint: In this question, we have \[4\] matchsticks.
We need to find out whether we can construct a triangle using match sticks or not and we have to use all the available matchsticks. First, we need to consider the conditions for making a triangle then consider if we can make it by giving matchsticks or not.

Complete step by step answer:
It is given that there are \[4\] matchsticks.
We need to find out whether we can construct a triangle using \[4\] match sticks or not and we have to use all the available matchsticks.
We know that to make a triangle we need three sides and the sum of two sides will be greater than the third side. (Triangle inequality property)
If we construct the triangle with \[4\] matchsticks it looks like the following:

Here, a = Length of the first side of the triangle = \[1\] matchstick
b = length of the second side of the triangle = \[1\] matchstick
c = length of the third side of the triangle = \[2\] matchstick
$a + b = 2$ matchsticks \[ = 1\] match stick \[ + 1\] match stick
Hence, the sum of the two sides isn’t greater than the third side.
Thus, the triangle is not possible.

Note: We have to know that, in mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
If a side is adequate to the opposite two sides, it’s not a triangle (just a straight line back and forth).