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:

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

It means that the hypotenuse is:

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

And the leg is:

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