Notes
Practice Problems
\({\textbf{1)}}\)\(\text{A triangle has sides with length }2,3, \text{ and } 4.\)
It is an obtuse triangle.
\(\,\,\,\,\,\text{Check }a+b \gt c\)
\(\,\,\,\,\,2+3 \gt 4\)
\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)
\(\,\,\,\,\,(2)^2+(3)^2 \bigcirc (4)^2\)
\(\,\,\,\,\,4+9 \bigcirc 16\)
\(\,\,\,\,\,13 \lt 16\)
\(\,\,\,\,\,\text{It is an obtuse triangle.}\)
\({\textbf{2)}}\)\(\text{A triangle has sides with length }7,8, \text{ and } 9.\)
It is an acute triangle.
\(\,\,\,\,\,\text{Check }a+b \gt c\)
\(\,\,\,\,\,7+8 \gt 9\)
\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)
\(\,\,\,\,\,(7)^2+(8)^2 \bigcirc (9)^2\)
\(\,\,\,\,\,49+64 \bigcirc 81\)
\(\,\,\,\,\,113 \gt 81\)
\(\,\,\,\,\,\text{It is an acute triangle.}\)
\({\textbf{3)}}\)\(\text{A triangle has sides with length }3,3, \text{ and } 5. \)
It is an obtuse triangle.
\(\,\,\,\,\,\text{Check }a+b \gt c\)
\(\,\,\,\,\,3+3 \gt 5\)
\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)
\(\,\,\,\,\,(3)^2+(3)^2 \bigcirc (5)^2\)
\(\,\,\,\,\,9+9 \bigcirc 25\)
\(\,\,\,\,\,18 \lt 25\)
\(\,\,\,\,\,\text{It is an obtuse triangle.}\)
\({\textbf{4)}}\)\(\text{A triangle has sides with length }7,7, \text{ and } 1. \)
It is an acute triangle.
\(\,\,\,\,\,\text{Check }a+b \gt c\)
\(\,\,\,\,\,1+7 \gt 7\)
\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)
\(\,\,\,\,\,(1)^2+(7)^2 \bigcirc (7)^2\)
\(\,\,\,\,\,1+49 \bigcirc 49\)
\(\,\,\,\,\,50 \gt 49\)
\(\,\,\,\,\,\text{It is an acute triangle.}\)
\({\textbf{5)}}\)\(\text{A triangle has sides with length }6,8, \text{ and } 10. \)
It is a right triangle.
\(\,\,\,\,\,\text{Check }a+b \gt c\)
\(\,\,\,\,\,6+8 \gt 10\)
\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)
\(\,\,\,\,\,(6)^2+(8)^2 \bigcirc (10)^2\)
\(\,\,\,\,\,36+64 \bigcirc 100\)
\(\,\,\,\,\,100 = 100\)
\(\,\,\,\,\,\text{It is an right Triangle.}\)
\({\textbf{6)}}\)\(\text{A triangle has sides with length }1,1, \text{ and } \sqrt{2}.\)
It is a right triangle.
\(\,\,\,\,\,\text{Check }a+b \gt c\)
\(\,\,\,\,\,1+1 \gt \sqrt{2}\)
\(\,\,\,\,\,a^2+b^2 \bigcirc c^2\)
\(\,\,\,\,\,(1)^2+(1)^2 \bigcirc \left(\sqrt{2}\right)^2\)
\(\,\,\,\,\,1+1 \bigcirc 2\)
\(\,\,\,\,\,2 = 2\)
\(\,\,\,\,\,\text{It is an right triangle.}\)
\({\textbf{7)}}\)\(\text{A triangle has sides with length }3,4, \text{ and } 8.\)
This is not a possible triangle.
\(\,\,\,\,\,\text{Check }a+b \gt c\)
\(\,\,\,\,\,(3)+(4)\lt 8\)
\(\,\,\,\,\,\text{Due to triangle inequality theorem, it is not a possible triangle.}\)
See Related Pages\(\)
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