## Algebra 1: Common Core (15th Edition)

To form a right triangle, the three side lengths must satisfy the equation $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the two shorter side lengths and $c$ is the longest side length. To find out which of the lengths below can form a right triangle, plug the lengths into the equation above and see if it holds true. Does $12^{2}+13^{2}=17^{2}$ ? $144+169=289$ ? $313\ne289$ The answer is not A. Does $3.2^{2}+5.6^{2}=6.4^{2}$ ? $10.24+31.36=40.96$ ? $41.6\ne40.96$ The answer is not B. Does $14^{2}+20^{2}=24^{2}$ ? $196+400=576$ ? $596\ne576$ The answer is not C. By process of elimination, we know the answer is D, and we can prove it by substituting and solving. $10^{2}+24^{2}=26^{2}$ $100+576=676$ $676=676$ The answer is D.