SOLUTION
Consider the triangle shown below
This question will be solved using Pythagorean Theorem
Considering traingle KLN it follows:
[tex]x^2=y^2+20^2[/tex]
Considering triangle LMN it follows:
[tex]x^2=26^2-z^2[/tex]
Equate the x² values
[tex]y^2+20^2=26^2-z^2[/tex]
Considering triangle KLM
[tex]z^2=y^2^{}+6^2[/tex]
Substitute the value of z² into the previous equation
[tex]y^2+20^2=26^2_{}-(y^2+6^2)[/tex]
Simplify the equation
[tex]\begin{gathered} y^2+20^2=26^2_{}-y^2-6^2 \\ y^2+y^2=26^2-6^2-20^2 \\ 2y^2=240 \\ y^2=120 \end{gathered}[/tex]
Substitute y² into x²=y²+20²
[tex]\begin{gathered} x^2=120+20^2 \\ x^2=120+400 \\ x^2=520 \\ x=\sqrt[]{520}^{} \\ x=2\sqrt[]{130} \end{gathered}[/tex]
Therefore the value of LN is
[tex]2\sqrt[]{130}[/tex]
