Which of these could be the lengths of side of a right triangle?
a. (5, 6, 11)
b. (5,7,12)
c. (5, 12, 13)
d. (6, 7, 13)
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1
Answer:
If a triangle is a right triangle, then the lengths of its sides satisfy the Pythagorean Theorem, a
2
+b
2
=c
2
. To determine which choice is correct, test each set of values by substituting them into the Pythagorean Theorem. Start with the first set of numbers: 3, 13, and 14.
3
2
+13
2
=14
2
9+169=196
178=196
Since the result is not a true equality, the first set of values does not represent the side lengths of a right triangle. Test the other four choices. The only values that satisfy the Pythagorean Theorem are 5, 12, and 13.
5
2
+12
2
=13
2
25+144=169
169=169
Step-by-step explanation:
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