Hello there,
- I just looked into the question and you are absolutely right whatever you inferred.
- I think the question might be wrong.
- The value of c should be greater than b.
- I guess it will like this:
![b = 16 \: \: \: c = 17 (1)/(3)](https://img.qammunity.org/2022/formulas/mathematics/college/w19b3e3fu8720s8oyq8f5m132fds28tmm2.png)
- The values should be like this.
- I am solving the equation by this:
![{a}^(2) = {c}^(2) - {b}^(2) \\ = > {a}^(2) = {(17 (1)/(3)) }^(2) - {(16)}^(2) \\ = > {a}^(2) = {( (52)/(3) )}^(2) - {(16)}^(2) \\ = > {a}^(2) = ( (52)/(3) - 16)( (52)/(3) + 16) \\ = > {a}^(2) = ( (52 - 48)/(3) )( (52 + 48)/(3) ) \\ = > {a}^(2) = (4)/(3) * (100)/(3) \\ = > {a}^(2) = (400)/(9) \\ = > a = \sqrt{ (400)/(9) } \\ = > a = (20)/(3) \\ = > a = 6 (2)/(3)](https://img.qammunity.org/2022/formulas/mathematics/college/qce57huwjezbe0tzgls3y1p42oul96dsym.png)
- So, the value of a is
![a = 6 (2)/(3)](https://img.qammunity.org/2022/formulas/mathematics/college/3q83bvnq767pn5rllohs3hnqm4jzx904i1.png)
Hope you could get an idea from it.
Doubt clarification - use comment section.