To solve this problem, we will use the following diagram as reference:
Using the Pythagorean theorem, we get that ( we will omit the units to simplify the calculations):
[tex]100^2=(x+68)^2+x^2.[/tex]
Therefore:
[tex]\begin{gathered} 100^2=x^2+136x+68^2+x^2, \\ 2x^2+136x+68^2-100^2=0, \\ 2x^2+136x-5376=0. \end{gathered}[/tex]
Using the quadratic formula, we get:
[tex]x=\frac{-136\pm\sqrt[]{136^2-4(2)(-5376)}}{2(2)}.[/tex]
Simplifying the above result, we get:
[tex]\begin{gathered} x_1=28, \\ x_2=-96. \end{gathered}[/tex]
Since, the negative solution has no meaning in the context of the problem, x=28 in.
Answer:
[tex]28in\text{.}[/tex]
