ANSWER
The length of EF is
[tex]24units[/tex]
EXPLANATION
The given triangle is a right angle triangle.
The hypotenuse is |ED|. The two shorter legs are |EF| and |DF|.
We can apply the Pythagoras Theorem to find the length of EF.
According to the Pythagoras Theorem,
[tex]
|EF|^2+|DF|^2=|DE|^2[/tex]
We now substitute the values in to the formula to obtain,
[tex]
|EF|^2+10^2=26^2[/tex]
This gives us,
[tex]
|EF|^2+100=676[/tex]
We now group like terms to obtain,
[tex]
|EF|^2=676 - 100[/tex]
The right hand side will evaluate to,
[tex]
|EF|^2=576[/tex]
We take the positive square root of both sides to obtain,
[tex]
|EF|= \sqrt{576}[/tex]
[tex]
|EF|= 24[/tex]
The correct answer is C.
