The list of side lengths that represent a right triangle is 7, 24, 25 and this can be determined by using the Pythagorean theorem.
Given :
A right-angle triangle.
Check all the options in order to determine the lengths that represent a right triangle.
A) 3,6,9
The Pythagorean theorem can be used in order to determine the lengths that represent a right triangle.
[tex]9^2=6^2+3^2[/tex]
81 = 36 + 9
81 [tex]\neq[/tex] 45
Therefore, this option is incorrect.
B) 7, 24, 25
The Pythagorean theorem can be used in order to determine the lengths that represent a right triangle.
[tex]25^2=24^2+7^2[/tex]
625 = 576 + 49
625 = 625
Therefore, this option is correct.
C) 5, 12, 14
The Pythagorean theorem can be used in order to determine the lengths that represent a right triangle.
[tex]14^2=12^2+5^2[/tex]
196 = 144 + 25
196 [tex]\neq[/tex] 169
Therefore, this option is incorrect.
D) 15, 16, 17
The Pythagorean theorem can be used in order to determine the lengths that represent a right triangle.
[tex]17^2=16^2+15^2[/tex]
289 = 256 + 225
289 [tex]\neq[/tex] 481
Therefore, this option is incorrect.
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