Question

The lengths of three line segments are 3.1 cm, 6.1 cm and x cm. If x is given to be a natural number, then find the minimum value of x, so that the formation of a triangle is possible with these line segments.​

Answer 1

Is your question , minimum & maximum value of THIRD side? And do you want these values from the set of natural (means COUNTING numbers)?

first side = 3, second side = 6, third side=?

We know, the sum of any 2 sides of a triangle is greater than the third side..

So, third side should be smaller than 3+ 6

ie, third side < 9 ……..(1)

But , third side + first side > 6

Or, third side + 3 > 6

=> third side > 3 ……….(2)

By(1) & (2)

Third side lies between 3 & 9

Maximum value is nearest to 9 & minimum value is nearest to 3.

In integer form: Maximum value of third side = 8 cm

& Minimum value of third side = 4 cm

Answer 2

Answer:

Step-by-step explanation:

Concept:

A line segment in geometry is a section of a line that has two clearly defined end points and contains every point on the line that lies within its confines. Half-open line segments contain exactly one of the endpoints, while closed line segments have both of the endpoints. Open line segments do not contain either of the endpoints. A line above the symbols for the two endpoints is frequently used in geometry to represent a line segment.

The sides of a triangle or a square are examples of line segments. A line segment is either an edge (of that polygon or polyhedron) if its end points are nearby vertices, or a diagonal more broadly when both of its end points are vertices of a polygon or polyhedron. A line segment is referred to as a chord when both of its end points are located on a curve, like a circle (of that curve).

Given:

The lengths of three line segments are 3.1 cm, 6.1 cm and x cm.

Find:

the minimum value of x.

Solution:

given that

first side $=3cm$, second $=6cm$, and third $=xcm$

We are aware that any two triangle sides added together equal more than the third side.

Therefore, the third side should be less than$3 + 6.$

i.e., $third side < 9$

therefore, $third side + first side > 6$

also,$third side + 3 > 6$

$third side > 3...... (2)$

By(1) & (2)

third side between numbers $3$ and $9$

The closest values for the maximum and minimum are $9$ and$3$, respectively.

Maximum value of the third side is$8 cm$ in integer form. The third side's minimum value is$4 cm$.

Hence the minimum value of x = 4cm.

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