Question

The height of the TV set is … inchesThe length of the TV set is … inches

Answer 1

The surface of the TV is depicted in the diagram below.

Then, according to the Pythagoras theorem.

`26^2=h^2+l^2`

And, according to the problem

`l=14+h`

We have two equations and two unknowns; therefore, we can solve the system.

`\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}`

Solve the quadratic equation as shown below

`\begin{gathered} \Rightarrow(h+24)(h-10)=0 \\ \Rightarrow h=-24,h=10 \end{gathered}`

But h is the height; thus, it has to be a positive quantity. Then, h=10

Finally, we need to find l

`\begin{gathered} h=10 \\ \Rightarrow l=14+10=24 \\ \Rightarrow l=24 \end{gathered}`

The answers are: height equal to 10 and length equal to 24.