Question

Fill in the steps to find the length of the hypotenuse

Answer 1

Hypotenuse is 13 units

Explanation:

» From pythogras theorem:

`{ \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) } = √(169) }} \\ { \tt{c = 13 \: units}}`

Answer 2

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 :

`{\longrightarrow{\pmb{\sf{{(a)}^(2) + {(b)}^(2) = {(c)}^(2)}}}}`

• 
  `\pink\star` a = 12 km
• 
  `\pink\star` b = 5 km
• 
  `\pink\star` c = ?

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

`\begin{gathered} \qquad{\longrightarrow{\sf{{(a)}^(2) + {(b)}^(2) = {(c)}^(2)}}}\\\\\qquad{\longrightarrow{\sf{{(12)}^(2) + {(5)}^(2) = {(c)}^(2)}}}\\\\\qquad{\longrightarrow{\sf{(12 * 12) + (5 * 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 = √(169)}}}\\\\\qquad{\longrightarrow{\sf{\underline{\underline{\purple{c = 13}}}}}}\end{gathered}`

Hence, the length of hypotenuse is 13.

`\rule{300}{2.5}`