Answer
D; 10, 24, 26
Work Step by Step
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.
