State if the three sides lengths form a right triangle. 10) 9, 7, √125 11) √65, 4, 9 12) 12, 2√26, 15 13)...
10) 9, 7, √125
11) √65, 4, 9
12) 12, 2√26, 15
13) 5√3, 5, 10
To determine if the sides form a right triangle, use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse.
For 9, 7, √125:
9² + 7² = 81 + 49 = 130
(√125)² = 125
Since 130 ≠ 125, these sides do not form a right triangle.
For √65, 4, 9:
(√65)² + 4² = 65 + 16 = 81
9² = 81
Since 81 = 81, these sides form a right triangle.
For 12, 2√26, 15:
12² + (2√26)² = 144 + 4*26 = 144 + 104 = 248
15² = 225
Since 248 ≠ 225, these sides do not form a right triangle.
For 5√3, 5, 10:
(5√3)² + 5² = 75 + 25 = 100
10² = 100
Since 100 = 100, these sides form a right triangle.
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