Which best describes the construction of a triangle if given the segment lengths of 10 cm, 5 cm, and 4 cm?

2 answers:

8 0

It can't be constructed.
The lengths of 4 cm and 5 cm add to 9 cm and that is one too centimeter too short to make an angle with the 3rd side.

7 0

Answer:

It is not possible to construct a triangle with the given side lengths.

Step-by-step explanation:

We have been given three segment lengths and we are asked to describe about the construction of a triangle with given lengths: 10 cm, 5 cm, and 4 cm.

We will use triangle inequality theorem to answer our given problem.

Triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

So let us check our given using triangle inequality theorem as:

$5+10>4$

$15>4$

Now check another side.

$5+4>10$

$9\ngtr 10$

Since the sum of our given two sides is less than third side, therefore, we can not construct a triangle with our given side lengths.

You might be interested in

nataly862011 [7]

The 2nd and 3rd term of an AP is found to be (a₂ = 95) and (a₃ = 110).

<h3>What is the sequence of AP arithmetic progression?</h3>

In Arithmetic Progression, the difference between the two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come across a few key concepts in AP that had been labeled as:

As shown below, the AP can also be referred to in terms of common differences.

The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × d
The arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].
Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.

Now, the given sequence is; 80, _, _, 125.

The series comprises of four given terms.

Let the first term be 'a₁' = 180.

The second term be 'a₂'.

The third term be 'a₃'.

And, the fourth term is 'a₄' = 125.

Use the nth term formula to find the common difference 'd'.

n-th term: an = a + (n − 1) × d

a₄ = a + (n - 1)d

125 = 80 + (4 - 1)d

45 = 3d

d = 15