Question

Can a triangle have sides with the given​ lengths? Explain.
​4ft, ​6ft, 14ft

Answer 1

I searched and found that there is something called "triangle inequality theorem", in which we add 2 sides of the triangle and see if the sum is greater than the third side, we do it with every side. If the result is greater than the 3rd side in all three cases, we can say that the sides of the triangle are valid.

Lets see if adding 4 and 6 gives a greater result than 14:

4 + 6 = 10

So no, it is smaller than 14, hence a triangle cannot have these sides. If it was greater than 14, then we could move to another test such as, is 4 + 14 > 6?

Answer 2

Given:

Three line segments of length 4ft, 6ft, and 14ft are given.

To Find:

Can these three line segments form a triangle?

Solution:

Criteria to form a triangle by three line segment

If the sum of the length of two sides is less than that of the third one then only

we can draw a triangle.

Let, length of the three sides be a, b, and c units.

Conditions to form a triangle

Please find the attachment.