Answer:
The missing dimension is
[tex]5[/tex]
Step-by-step explanation:
The Pythagorean Theorem states that
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ [/tex]
Note that c is the hypothenus (the hypothenus is always opposite to the right angle of a triangle)
Therefore
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {12}^{2} + {b}^{2} = {13}^{2} \\ 144 + {b}^{2} = 169 \\ {b}^{2} = 169 - 144 \\ {b}^{2} = 25[/tex]
[tex] \sqrt{ {b}^{2} } = \sqrt{25} \\ b = 5[/tex]
Therefore the missing dimension is 5
