Answer:
Option J 13
Step-by-step explanation:
we know that
If applying the Pythagoras Theorem
[tex]c^{2}> a^{2} +b^{2}[/tex] ----> is an obtuse triangle
[tex]c^{2}< a^{2} +b^{2}[/tex] ----> is an acute triangle
[tex]c^{2}= a^{2} +b^{2}[/tex] ----> is a right triangle
where
c is the greater side
Verify each case
case F) we have
[tex]c=10, a=6, b=8[/tex]
substitute
[tex]10^{2}> 6^{2} +8^{2}[/tex]
[tex]100> 100[/tex] -----> is not true
Is a right triangle
case G) we have
[tex]c=10, a=9, b=8[/tex]
substitute
[tex]10^{2}> 9^{2} +8^{2}[/tex]
[tex]100> 145[/tex] -----> is not true
Is an acute triangle
case H) we have
[tex]c=12, a=8, b=10[/tex]
substitute
[tex]12^{2}> 8^{2} +10^{2}[/tex]
[tex]144> 164[/tex] -----> is not true
Is an acute triangle
case J) we have
[tex]c=13, a=8, b=10[/tex]
substitute
[tex]13^{2}> 8^{2} +10^{2}[/tex]
[tex]169> 164[/tex] -----> is true
Is an obtuse triangle
