Answer:
c = [tex]{\boxed{\boldsymbol{29}}}[/tex] km
Step-by-step explanation:
Here's the required formula to find the missing side of triangle by pythagoras theorem :
[tex]{\longrightarrow{\pmb{\sf{{(a)}^{2} + {(b)}^{2} = {(c)}^{2}}}}}[/tex]
- [tex]\purple\star[/tex] a = 20 km
- [tex]\purple\star[/tex] b = 21 km
- [tex]\purple\star[/tex] c = ?
Substituting all the given values in the formula to find the third side of triangle :
[tex] \begin{gathered} \quad{\longrightarrow{\sf{{(a)}^{2} + {(b)}^{2} = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{{(20)}^{2} + {(21)}^{2} = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{(20 \times 20) + (21 \times 21) = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{(400) + (441) = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{400 + 441 = {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{841= {(c)}^{2}}}} \\ \\ \quad{\longrightarrow{\sf{c = \sqrt{841}}}} \\ \\ \quad{\longrightarrow{\sf{\underline{\underline{\purple{c = 29 \: km}}}}}}\end{gathered}[/tex]
Hence, the length of missing side of triangle is 29 km.
[tex]\rule{300}{2.5}[/tex]
