Answer :

brainsoft

Answer:

Hypotenuse is 13 units

Step-by-step explanation:

» From pythogras theorem:

[tex]{ \tt{ {c}^{2} = {a}^{2} + {b}^{2} }} \\ { \tt{ {c}^{2} = {12}^{2} + {5}^{2} }} \\ { \tt{ {c}^{2} = 144 + 25 }} \\ { \tt{ {c}^{2} = 169 }} \\ { \tt{ \sqrt{ {c}^{2} } = \sqrt{169} }} \\ { \tt{c = 13 \: units}}[/tex]

AadhPrit

Answer:

The length of hypotenuse is 13.

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]\pink\star[/tex] a = 12 km
  • [tex]\pink\star[/tex] b = 5 km
  • [tex]\pink\star[/tex] c = ?

Substituting all the given values in the formula to find the hypotenuse of triangle :

[tex]\begin{gathered} \qquad{\longrightarrow{\sf{{(a)}^{2} + {(b)}^{2} = {(c)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{{(12)}^{2} + {(5)}^{2} = {(c)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{(12 \times 12) + (5 \times 5) = {(c)}^{2}}}} \\ \\ \qquad{\longrightarrow{\sf{(144) +(25) = {(c)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{144 + 25 = {(c)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{169 = {(c)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{c = \sqrt{169}}}}\\\\\qquad{\longrightarrow{\sf{\underline{\underline{\purple{c = 13}}}}}}\end{gathered}[/tex]

Hence, the length of hypotenuse is 13.

[tex]\rule{300}{2.5}[/tex]