Respuesta :
The correct option is c.
Given to us
- 4,5,6
- 8,10,12
- 5,12,13
- 5,10,12
Pythagoras theorem.
For a triangle to be a right-angled triangle it should follow the Pythagoras theorem.
a.) 4, 5, 6
H = 6, as it is the longest side of the triangle, therefore,
[tex]\\H^2 = 6^{2} \\B^2+P^2 = 5^2+4^2=41\\\\36 \neq 41[/tex]
As we can see that the hypotenuse square is not equal to the base square and perpendicular square, therefore, this can not be a right-angled triangle.
b.) 8, 10, 12
H = 12, as it is the longest side of the triangle, therefore,
[tex]\\H^2 = 12^{2} \\B^2+P^2 = 8^2+10^2=164\\\\144 \neq 164[/tex]
As we can see that the hypotenuse square is not equal to the base square and perpendicular square, therefore, this can not be a right-angled triangle.
c.) 5, 12, 13
H = 13, as it is the longest side of the triangle, therefore,
[tex]\\H^2 = 13^{2} \\B^2+P^2 = 5^2+12^2=169\\\\144 =169[/tex]
As we can see that the hypotenuse square is equal to the base square and perpendicular square, therefore, this is a right-angled triangle.
d.) 5, 10, 12
H = 12, as it is the longest side of the triangle, therefore,
[tex]\\H^2 = 12^{2} \\B^2+P^2 = 5^2+10^2=125\\\\125\neq 144[/tex]
As we can see that the hypotenuse square is not equal to the base square and perpendicular square, therefore, this can not be a right-angled triangle.
Hence, the correct option is c.
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