Question

The two legs of a right triangle are the same length. The hypotenuse is 5 meters long. Find the length of the legs, Express your answer in simplified radical form, onadecimal rounded to four places

Answer 1

Given a right angle triangle with equal legs and the hypotenuse as 5 meters, we can proceed to draw a diagram to help illustrate the solution.

Let the value of the legs be x

We can find the value of x using the Pythagoras theorem.

`\begin{gathered} 5^2=x^2+x^2 \\ 2x^2=25 \\ \text{Divide both sides by 2} \\ x^2=(25)/(2) \\ \text{square root both sides} \\ x=\sqrt[]{(25)/(2)} \\ x=\frac{5}{\sqrt[]{2}} \\ we\text{ find the conjugate of the radical} \\ \frac{5}{\sqrt[]{2}}*\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ \therefore x=\frac{5\sqrt[]{2}}{2} \end{gathered}`

Therefore, the length of the leg is

`x=\frac{5\sqrt[]{2}}{2}`