Question

The hypotenuse of a right triangle is twice the length of one of its legs.The length of the other leg is three feet.Find the lengths of the three sides of the triangle.Round to the nearest tenth.

Short answer

The lengths of the three sides of the triangle are$3,\sqrt{3}\mathrm{and}2\sqrt{3}$

Step-by-step solution

Given information

The given statement is the hypotenuse of a right triangle is twice the length of one of its legs.The length of the other leg is three feet.

Take x be the length of one of its legs.length of the other leg is three feet.Hypotenuse as 2x.

By using Pythagoras Theorem

$$\begin{gathered} {\left(x\right)}^2+{\left(3\right)}^2={\left(2x\right)}^2 \\ {x}^2+9=4x^2 \\ 9=4x^2-x^2 \\ 3x^2=9 \\ {x}^2=3 \\ x=\pm \sqrt{3} \end{gathered}$$

Hypotenuse =$2\left(\sqrt{3}\right)$