Answer: The length is 12 inches while the height is 5 inches
Step-by-step explanation: It the Television has a diagonal of 13 inches, and a height of H inches, then the length would be (H + 7) inches. It’s length is 7 inches more than the height. At this point we can draw up a right angled triangle with the hypotenuse as 13 (diagonal side) and the other two sides as H and (H + 7)
Then we can apply the Pythagoras theorem which states that
AC^2 = AB^2 + BC^2
(Where AC is the hypotenuse and AB and BC are the two other sides)
Hence,
13^2 = H^2 + (H + 7)^2
169 = H^2 + (H^2 + 14H + 49)
169 = 2H^2 + 14H + 49
By collecting like terms we now have
169 - 49 = 2H^2 + 14H
120 = 2H^2 + 14H
By re-arranging all terms on one side of the equation, we arrive at
2H^2 + 14H - 120 = 0
Divide all sides by 2
H^2 + 7H - 60 = 0
To solve the quadratic equation, we now factorize and we have,
H^2 + 12H - 5H - 60 = 0
(H + 12) (H - 5) = 0
Therefore
Either H + 12 = 0 OR
H - 5 = 0
Hence, Either H = -12 or H = 5
The dimension can not be a negative value so we shall take h equals 5.
Having calculated the height of the television as 5 inches, the length which was given as H + 7 can now be calculated as
Length = H + 7
Length = 5 + 7
Length = 12
Therefore, the length of the Television is 12 inches and the height is 5 inches
