Final answer:
The length of a 62-inch TV with an aspect ratio of 4:3 is found to be approximately 49.6 inches using the Pythagorean theorem to solve for the scaling factor and then multiplying it by 4.
Step-by-step explanation:
The student is asking for the length of the TV given its diagonal size and aspect ratio. The TV has a diagonal size of 62 inches and an aspect ratio of 4:3. Since the aspect ratio can be written as L:W (Length:Width), we can use the Pythagorean theorem to find the length. The length (L) and width (W) of the TV can be defined as L = 4x and W = 3x, where x is a scaling factor.
Using the Pythagorean theorem for a right triangle, we have:
L2 + W2 = Diagonal2
This can be written as: (4x)2 + (3x)2 = 622
Which simplifies to: 16x2 + 9x2 = 3844
Combining like terms we get: 25x2 = 3844
Divide both sides by 25 to get: x2 = 153.76
Now we find the square root of 153.76 which gives us x ≈ 12.4.
We can now calculate the length using L = 4x: L = 4(12.4) ≈ 49.6 inches.
So, the length of the TV is approximately 49.6 inches.