Question

State an equation you could use to find the value of $x$. Then find the value of $x$ in simplest radical form.

Short answer

The required value of $x$ is,

$x=12$.

Step-by-step solution

Step 1. Given information.

We have given a figure as shown below.

Step 2. Use Pythagorean Theorem concept.

From Pythagorean Theorem,

we know that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

The given triangle is right triangle.

Therefore,

$\begin{array}{c}{5}^2+x^2={\left(x+1\right)}^2\\ 25+x^2=x^2+2x+1\\ 25=2x+1\\ 25-1=2x\\ 24=2x\\ x=12\end{array}$

Step 3. Neglect negative sign.

Since, square root is positive quantity

So, we neglect negative sign.

Therefore, the required value of $x$ is, $x=12$.