Question

A tile mosaic in the shape of a right triangle is used as the corner of a rectangular pathway.

The hypotenuse of the mosaic is $5$ft.one side of the mosaic is twice as long as the other side. What are the lengths of the sides? Round to the nearest tenth.

Short answer

The length of one leg is$2.2$ft and the length of the second leg is$4.4$ft.

Step-by-step solution

Step 1. Given information.

one side of the mosaic is twice as long as the other side. The hypotenuse of the mosaic is$5$ ft.

Step 2. Determine the length of the sides.

From the given information:

one side of the mosaic is twice as long as the other side.

Let the length of one leg is $s$.

The length of the second leg is$2s$.

Step 3. Apply Pythagorean theorem to frame the equation.

From the given figure:

$\begin{array}{rcl}{s}^2+{\left(2s\right)}^2& =& {\left(5\right)}^2\\ s^2+4s^2& =& 25\\ 5s^2& =& 25\end{array}$

Step 4. Solve the equation for s.

$\begin{array}{rcl}5s^2& =& 25\\ s^2& =& \frac{25}{5}\\ s^2& =& 5\\ s& =& \pm \sqrt{5}\\ s& \approx & \pm 2.2\end{array}$

The length can't be negative.

So, the required value of length is$s=2.2$.

Step 5. Simplified answer.

Hence, the length of one leg is $s=2.2ft$.

The length of the second leg is:

$\begin{array}{rcl}2s& =& 2\left(2.2\right)\\ & =& 4.4ft\end{array}$