The surface of the TV is depicted in the diagram below.
Then, according to the Pythagoras theorem.
[tex]26^2=h^2+l^2[/tex]
And, according to the problem
[tex]l=14+h[/tex]
We have two equations and two unknowns; therefore, we can solve the system.
[tex]\begin{gathered} l=14+h \\ \Rightarrow26^2=h^2+(14+h)^2 \\ \Rightarrow26^2=h^2+14^2+28h+h^2 \\ \Rightarrow2h^2+28h-480=0 \\ \Rightarrow h^2+14h-240=0 \end{gathered}[/tex]
Solve the quadratic equation as shown below
[tex]\begin{gathered} \Rightarrow(h+24)(h-10)=0 \\ \Rightarrow h=-24,h=10 \end{gathered}[/tex]
But h is the height; thus, it has to be a positive quantity. Then, h=10
Finally, we need to find l
[tex]\begin{gathered} h=10 \\ \Rightarrow l=14+10=24 \\ \Rightarrow l=24 \end{gathered}[/tex]
The answers are: height equal to 10 and length equal to 24.
