Answer: 21 , 72 , 75
Step-by-step explanation:
The one that could represent the three sides of a right angle triangle must obey Pythagoras theorem , that is
[tex]a^{2}+b^{2}=c^{2}[/tex]
a = side of right triangle
b = side of right triangle
c = hypotenuse
Let's check the sides one after the other
1. [tex]21 , 72 , 75[/tex]
[tex]21^{2}+72^{2} = 5,625[/tex]
[tex]75^{2}=5625[/tex]
this means that
[tex]21^{2}+72^{2}=75^{2}[/tex]
this could represent the three sides of a right triangle
2. [tex]7,8,10[/tex]
[tex]7^{2}+8^{2}=113[/tex]
[tex]10^{2}=100[/tex]
[tex]7^{2}+8^{2}\neq 10^{2}[/tex]
3. [tex]8, 12 , 15[/tex]
[tex]8^{2}+12^{2}= 208[/tex]
[tex]15^{2}=225[/tex]
[tex]8^{2}+12^{2}\neq 15^{2}[/tex]
4. [tex]14,84,85[/tex]
[tex]14^{2}+84^{2}=7,252[/tex]
[tex]85^{2} = 7225[/tex]
[tex]14^{2}+84^{2}\neq 85^{2}[/tex]
Therefore , the only combination that could represent the three sides of a right triangle will be 21 , 72 , 75
