Question

The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is 7 feet. Find tje length of the three sides of the triangle. Answer exactly or round to 2 decimal places. The legs of the triangle are 7_ feet and the hypotenuse is _ feet

Answer 1

Taking l as the length of one of the legs and using the pythagorean theorem we have that:

`(2l)^2=l^2+7^2`

Solve the equation for l:

`\begin{gathered} 4l^2=l^2+49 \\ 4l^2-l^2=49 \\ 3l^2=49 \\ l^2=(49)/(3) \\ l=\sqrt[]{(49)/(3)} \\ l=\frac{7}{\sqrt[]{3}}=\frac{7\sqrt[]{3}}{3} \end{gathered}`

It means that the hypotenuse is:

`\frac{14\sqrt[]{3}}{3}`

And the leg is:

`\frac{7\sqrt[]{3}}{3}`