To find the dimensions of the TV set, we can set up a system of equations based on the given information.
Let's assume the height of the TV set is represented by h inches.
According to the given information, the length of the TV set is 14 inches more than the height. Therefore, the length would be h + 14 inches.
We also know that the diagonal of the TV set is 26 inches.
Using the Pythagorean theorem, we can relate the height, length, and diagonal of the TV set:
(diagonal)^2 = (height)^2 + (length)^2
Substituting the given values, we have:
26^2 = h^2 + (h + 14)^2
676 = h^2 + (h + 14)^2
Expanding the equation, we get:
676 = h^2 + (h^2 + 28h + 196)
Combining like terms:
2h^2 + 28h + 196 = 676
2h^2 + 28h + 196 - 676 = 0
2h^2 + 28h - 480 = 0
Dividing the equation by 2 to simplify:
h^2 + 14h - 240 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula.
Factoring the equation, we have:
(h - 8)(h + 30) = 0
From this, we get two possible solutions for h:
h - 8 = 0 OR h + 30 = 0
h = 8 OR h = -30
Since the dimensions of a TV cannot be negative, we discard the second solution and solve for h = 8.
Therefore, the height of the TV set is 8 inches.
Now, let's find the length of the TV set using the equation:
Length = Height + 14
Length = 8 + 14
Length = 22 inches
So, the dimensions of the TV set are 8 inches (height) and 22 inches (length).