College

We appreciate your visit to Select the correct answer A triangle has one side of length 29 units and another of length 40 units Determine the range in which the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Select the correct answer.

A triangle has one side of length 29 units and another of length 40 units. Determine the range in which the length of the third side must lie.

A. [tex]-11 \ \textless \ x \ \textless \ 69[/tex]
B. [tex]11 \leq x \leq 69[/tex]
C. [tex]11 \ \textless \ x \ \textless \ 69[/tex]
D. [tex]-11 \leq x \leq 69[/tex]

Answer :

To determine the possible length of the third side, denoted as [tex]$x$[/tex], you use the triangle inequality. The triangle inequality states that for any triangle with sides of lengths [tex]$a$[/tex], [tex]$b$[/tex], and [tex]$c$[/tex], the following must hold:

[tex]$$|a - b| < c < a + b$$[/tex]

Here, you are given two sides with lengths [tex]$29$[/tex] and [tex]$40$[/tex]. Let these be [tex]$a$[/tex] and [tex]$b$[/tex], and let [tex]$x$[/tex] be the length of the third side. Then:

1. Calculate the absolute difference:
[tex]$$|29 - 40| = 11$$[/tex]

2. Calculate the sum:
[tex]$$29 + 40 = 69$$[/tex]

Therefore, the third side must satisfy:
[tex]$$11 < x < 69$$[/tex]

This corresponds to option C:
[tex]$$11 < x < 69$$[/tex]

So, the correct answer is option C.

Thanks for taking the time to read Select the correct answer A triangle has one side of length 29 units and another of length 40 units Determine the range in which the. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada