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!
Answer :
Sure, we can determine the range of the third side of a triangle using the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This leads to a few key inequalities based on a triangle with sides [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
1. [tex]\(a + b > c\)[/tex]
2. [tex]\(a + c > b\)[/tex]
3. [tex]\(b + c > a\)[/tex]
For our triangle, we have two known sides: 29 units and 40 units. We need to find the possible range for the third side, which we'll call [tex]\(x\)[/tex].
Using the inequalities:
1. [tex]\(29 + 40 > x \Rightarrow x < 69\)[/tex]
2. [tex]\(29 + x > 40 \Rightarrow x > 11\)[/tex]
3. [tex]\(40 + x > 29 \Rightarrow x > -11\)[/tex] (This inequality isn't useful in this case since [tex]\(x > 11\)[/tex] is a tighter constraint.)
The useful inequalities are:
- [tex]\(x < 69\)[/tex] from the first inequality.
- [tex]\(x > 11\)[/tex] from the second inequality.
Therefore, by combining these, the length of the third side must lie in the range [tex]\(11 < x < 69\)[/tex].
The correct answer is:
C. [tex]\(11 < x < 69\)[/tex]
1. [tex]\(a + b > c\)[/tex]
2. [tex]\(a + c > b\)[/tex]
3. [tex]\(b + c > a\)[/tex]
For our triangle, we have two known sides: 29 units and 40 units. We need to find the possible range for the third side, which we'll call [tex]\(x\)[/tex].
Using the inequalities:
1. [tex]\(29 + 40 > x \Rightarrow x < 69\)[/tex]
2. [tex]\(29 + x > 40 \Rightarrow x > 11\)[/tex]
3. [tex]\(40 + x > 29 \Rightarrow x > -11\)[/tex] (This inequality isn't useful in this case since [tex]\(x > 11\)[/tex] is a tighter constraint.)
The useful inequalities are:
- [tex]\(x < 69\)[/tex] from the first inequality.
- [tex]\(x > 11\)[/tex] from the second inequality.
Therefore, by combining these, the length of the third side must lie in the range [tex]\(11 < x < 69\)[/tex].
The correct answer is:
C. [tex]\(11 < x < 69\)[/tex]
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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
