9. which of the following could be the side measures of a right triangle?
a. 5 ft, 4 ft, 3 ft
c. 11 ft, 10 ft, 6 ft
b. 6 ft, 4 ft, 2 ft
d. 15 ft, 10 ft, 5 ft

  A.  5 ft, 4 ft, 3 ft

Step-by-step explanation:

When you use the Pythagorean theorem with the numbers of the first choice, you find that these could be the sides of a right triangle:

  3² + 4² = 9 + 16 = 25 = 5²

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You have found the correct answer at this point.

If you want to check, you can examine the other choices:

  C: 6² +10² = 136 ≠ 11²

  B: 2² +4² = 20 ≠ 6²

  D: 5² +10² = 125 ≠ 15²

Comment on 3-4-5 triangle

As you can see from the above, side measures of 3, 4, and 5 will form a right triangle. This is the smallest set of integers that will do so. It is also the ratios of the only set of side lengths in arithmetic progression that will do so.

This latter fact can help you rule out choices B and D in this problem, because each of those has sides in the progression 1 : 2 : 3.

(3, 4, 5) triangles come up often in algebra and geometry problems. This is a useful "Pythagorean triple" to remember.

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