Question

The hypotenuse of a triangle is 12 feet long. One leg is 6 feet long. What is the length of the other leg? Express youranswer in simplest radical form.ISubmitaINTLb1145

Answer 1

The formual for the pythagoras theorem with 'c' as hypotenuse, 'b' as base and 'a' as altitude is,

`c^2=a^2+b^2`

Substitute 12 for c and 6 for b to determine the length of other leg by using the pythagoras theoem.

`\begin{gathered} (12)^2=a^2+(6)^2 \\ 144-36=a^2 \\ a^2=108 \\ a=\sqrt[]{108} \\ a=\sqrt[]{6\cdot6\cdot3} \\ =6\sqrt[]{3} \end{gathered}`

The answer is,

`6\sqrt[]{3}\text{ feet}`