You are deciding between purchasing two TVs at the store that cost the same price. One TV you physically measure to be 32 inches long by 56 inches wide. The second TV is in box only and advertises itself as 39 inches long by 52 inches wide. Knowing that TVs are traditionally measured by their diagonal length, you want to know which TV is the larger TV.

Question

You are deciding between purchasing two TVs at the store that cost the same price. One TV you physically measure to be 32 inches long by 56 inches wide. The second TV is in box only and advertises itself as 39 inches long by 52 inches wide. Knowing that TVs are traditionally measured by their diagonal length, you want to know which TV is the larger TV.

Answer 1

To determine which TV is larger, we need to compare their diagonal lengths, as that is the traditional measure used for TVs.

Using the Pythagorean theorem (a² + b² = c²) where c represents the diagonal length, we can calculate the diagonal lengths for both TVs.

For the first TV:
a = 32 inches (length)
b = 56 inches (width)
c¹ = √(32² + 56²)

For the second TV:
a = 39 inches (length)
b = 52 inches (width)
c² = √(39² + 52²)

Calculating these values, we find:
c¹ ≈ 66.8 inches (rounded)
c² ≈ 64.81 inches (rounded)

Comparing the two diagonal lengths, we can conclude that the TV with a diagonal length of approximately 66.8 inches is larger than the TV with a diagonal length of approximately 64.81 inches.

Therefore, based on the traditional measure used for TVs, the first TV (32x56) is larger than the second TV (39x52).

Answer 2

To compare the sizes of the two TVs, we can calculate their diagonal lengths using the given measurements.

For the first TV, which has physical measurements of 32 inches long by 56 inches wide, we can use the Pythagorean theorem to calculate the diagonal length (d):
d^2 = 32^2 + 56^2
d^2 = 1024 + 3136
d^2 = 4160
d ≈ 64.49 inches

For the second TV, which is advertised as 39 inches long by 52 inches wide, we can again use the Pythagorean theorem to calculate the diagonal length (d):
d^2 = 39^2 + 52^2
d^2 = 1521 + 2704
d^2 = 4225
d ≈ 65 inches

Comparing the two diagonal lengths, we can determine that the second TV with the advertised measurements is slightly larger, with a diagonal length of approximately 65 inches, while the first TV has a diagonal length of approximately 64.49 inches.

Answer 3

To determine which TV is larger, you need to compare their diagonal lengths. TVs are typically measured diagonally from one corner to the opposite corner of the screen.

For the first TV, you have the width (56 inches) and length (32 inches). To find the diagonal length, you can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, you can calculate the diagonal length (d) of the first TV using the following formula:

d = √(width² + length²)

For the first TV:
d = √(56² + 32²)
d = √(3136 + 1024)
d = √(4160)
d ≈ 64.5 inches

Therefore, the diagonal length of the first TV is approximately 64.5 inches.

For the second TV, you have the advertised lengths. The diagonal length (d) can be found using the same formula:

d = √(width² + length²)

For the second TV:
d = √(52² + 39²)
d = √(2704 + 1521)
d = √(4225)
d ≈ 65 inches

Therefore, the diagonal length of the second TV is approximately 65 inches.

Comparing the diagonal lengths of the two TVs, we can determine that the second TV (advertised as 39 inches long by 52 inches wide) has a slightly larger screen size with a diagonal length of approximately 65 inches, compared to the first TV's diagonal length of approximately 64.5 inches.