Question

Find the third side of a right triangle that has a leg measuring 5 cm and hypotenuse measuring 13 cm.

Answer 1

Our answer is b = 12.

`\Large\texttt{Explanation}`

We are asked to find the third side of a right triangle, given the other two sides:

`\sf{5\;cm\quad\;and\quad\sf{13\;cm}`

Use the Pythagorean theorem (
`\sf{a^2+b^2=c^2}`), where a and b are the legs and c is the hypotenuse.

Plug in the values -

`\sf{5^2+b^2=13^2}`

Solve for b.

`\begin{gathered}\sf{25+b^2=169}\\\sf{b^2=169-25}\\\sf{b^2=144}\\\sf{b=12}\end{gathered}`

`\therefore` b = 12

Answer 2

third side = 12 cm

Explanation:

using Pythagoras' identity in the right triangle

a² + b² = c²

a, b are the legs and c the hypotenuse

given

one leg = 5 cm , hypotenuse = 13 cm

let the third leg be x

substituting these values , gives

x² + 5² = 13²

x² + 25 = 169 ( subtract 25 from both sides )

x² = 144 ( take square root of both sides )

`√(x^2)` =
`√(144)`

x = 12

Then the third side is 12 cm