Question

The two legs of a right triangle are the same length. The hypotenuse is 3 meters long. Find the length of the legs, Express your answer insimplified radical form, or as a decimal rounded to four places.

Answer 1

To solve this question, we will apply Pythagoras theorem, which states that:

`Hypotenuse^2=Opposite^2+Adjacent^2`

- We are given that:

`\begin{gathered} Hypotenuse=3 \\ Opposite=Adjacent=x \end{gathered}`

- Thus, we can say:

`\begin{gathered} 3^2=x^2+x^2 \\ 2x^2=9 \\ \text{ Divide both sides by 2} \\ x^2=(9)/(2) \\ \\ Take\text{ the square root of both sides} \\ x=\sqrt{(9)/(2)}=(3)/(√(2)) \\ \\ x=(3)/(√(2))*(√(2))/(√(2)) \\ \\ x=(3)/(2)√(2) \end{gathered}`

Final Answer

The length of the legs are:

`(3)/(2)√(2)`