3
AssignmentMultiple Select

Converse to the Pythagorean Theorem

Question 3 • ELPGEQ1 M/J Grade 8 Pre-Algebra - 1205070 HCPS V24

Which of the following triangle lengths form right triangles? Select all that apply.

Answer
A
(7, 11, 13)
B
(10, 24, 26)
C
(12, 16, 20)
D
(12, 35, 37)
E
(13, 15, 19)

Explanation

For each set, use the largest length as the possible hypotenuse and check whether the squares of the other two lengths add to its square. For (10, 24, 26), 10² + 24² = 676 = 26²; for (12, 16, 20), 12² + 16² = 400 = 20²; and for (12, 35, 37), 12² + 35² = 1,369 = 37². The other sets do not satisfy this rule, so the correct choices are (10, 24, 26), (12, 16, 20), and (12, 35, 37).

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