Question

In the following exercises, solve by using methods of factoring, the square root principle, or the quadratic formula.

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 feet. 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 side is$2.2ft.$and the length of the other side is$4.4ft.$

Step-by-step solution

Given information.

The given statement is:

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 feet. 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.

Set up an equation such that the length of one side is twice the other.

Let the length of one side be $s$and the length of the other side be$\left(2s\right).$

In the right triangle, the hypotenuse is $5feet$and the length of the sides is$sand2s.$

Use the Pythagoras theorem.

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

Solve for the value of $x.$

$$\begin{gathered} s^2=\frac{25}{5} \\ {s}^2=5 \end{gathered}$$

Using the square root property.

$$\begin{gathered} s=\pm \sqrt{5} \\ s=-2.2,2.2 \end{gathered}$$

The length cannot be negative. So, the length of one side is $2.2ft.$and the second side is $2.2\times 2=4.4ft.$