Answer:
B. [tex]10[/tex] cm, [tex]15[/tex] cm, [tex]24[/tex] cm
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of two sides of a triangle must always be greater than the length of the third side
so
[tex]a+b > c[/tex]
[tex]a+c > b[/tex]
[tex]b+c >a[/tex]
where
a,b,c are the lengths sides of the triangle
case A) [tex]6[/tex] cm, [tex]23[/tex] cm, [tex]11[/tex] cm
Let
[tex]a=6\ cm[/tex]
[tex]b=23\ cm[/tex]
[tex]c=11\ cm[/tex]
Verify
[tex]a+b > c[/tex] ------> [tex]6+23 > 11[/tex] ------> is true
[tex]a+c > b[/tex] ------> [tex]6+11 > 23[/tex] -------> is not true
therefore
The three lengths of case A) could not be the lengths of the sides of a triangle
case B) [tex]10[/tex] cm, [tex]15[/tex] cm, [tex]24[/tex] cm
Let
[tex]a=10\ cm[/tex]
[tex]b=15\ cm[/tex]
[tex]c=24\ cm[/tex]
Verify
[tex]a+b > c[/tex] ------> [tex]10+15 > 24[/tex] ------> is true
[tex]a+c > b[/tex] ------> [tex]10+24 > 15[/tex] -------> is true
[tex]b+c >a[/tex] -----> [tex]15+24 >10[/tex] --------> is true
therefore
The three lengths of case B) could be the lengths of the sides of a triangle
case C) [tex]22[/tex] cm, [tex]6[/tex] cm, [tex]6[/tex] cm
Let
[tex]a=22\ cm[/tex]
[tex]b=6\ cm[/tex]
[tex]c=6\ cm[/tex]
Verify
[tex]a+b > c[/tex] ------> [tex]22+6 > 6[/tex] ------> is true
[tex]a+c > b[/tex] ------> [tex]22+6> 6[/tex] -------> is true
[tex]b+c >a[/tex] -----> [tex]6+6 >22[/tex] --------> is not true
therefore
The three lengths of case C) could not be the lengths of the sides of a triangle
case D) [tex]15[/tex] cm, [tex]9[/tex] cm, [tex]24[/tex] cm
Let
[tex]a=15\ cm[/tex]
[tex]b=9\ cm[/tex]
[tex]c=24\ cm[/tex]
Verify
[tex]a+b > c[/tex] ------> [tex]15+9 > 24[/tex] ------> is not true
therefore
The three lengths of case D) could not be the lengths of the sides of a triangle
