Question 597439: Which measures would be the side lengths of a right triangle?
A. 2 cm, 5 cm, 7 cm
B. 9 cm, 14 cm, 17 cm
C. 7 cm, 17 cm, 24 cm
D. 5 cm, 12 cm, 13 cm
Found 2 solutions by rapaljer, AnlytcPhil:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! It it is a right triangle, then by Theorem of Pythagoras,  .
In this case, this is true ONLY in D. 5 cm, 12 cm, 13 cm.
For additional explanation on THEOREM of PYTHAGORAS, see my non-traditional explanation that is available FREE on my own website. The easiest way to find the website is to use the easy to spell and easy to remember link www.mathinlivingcolor.com. On this single page website, there is a link at the bottom of the page that takes you to my Homepage.
Near the top of my homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", and choose Basic Algebra (Chapter 2). Look for Section 2.10 THEOREM OF PYTHAGORAS.
There you will find explanations that may be easier to understand than your traditional textbooks, and many of the exercises from these sections are solved in color on the "MATH IN LIVING COLOR" pages that go with these sections.
If you like my website, please tell your friends and family. It's all FREE. You can contact me by Email at rapaljer@seminolestate.edu.
Dr. Robert J. Rapalje, Retired Professor of Mathematics
Seminole State College of Florida
Answer by AnlytcPhil(1806)  (Show Source):
You can put this solution on YOUR website!
We check each to see if the Pythagorean equation is true or false:
 +  = 
A. 2 cm, 5 cm, 7 cm
2² + 5² = 7²
4 + 25 = 49
29 = 49
False, so A is not the correct choice
B. 9 cm, 14 cm, 17 cm
9² + 14² = 17²
81 + 196 = 289
277 = 289
False, so B is not the correct choice
C. 7 cm, 17 cm, 24 cm
7² + 17² = 24²
49 + 289 = 576
338 = 576
False, so C is not the correct choice
D. 5 cm, 12 cm, 13 cm
5² + 12² = 13²
25 + 144 = 169
169 = 169
True, so D is the correct choice
Edwin
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