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 a box only and advertises itself as 39 inches long and 52 inches wide, knowing that TVs are traditionally measured by the diagonal length you want to know which TV is the larger TV.
To determine which TV is larger, we will compare their diagonal lengths.
For the first TV, which you physically measured, we can use the Pythagorean theorem to calculate the diagonal length:
diagonal^2 = length^2 + width^2
diagonal^2 = 32^2 + 56^2
diagonal^2 = 1024 + 3136
diagonal^2 = 4160
diagonal ≈ 64.49 inches
For the second TV, which is advertised as 39 inches long and 52 inches wide, the diagonal length can be calculated similarly:
diagonal^2 = length^2 + width^2
diagonal^2 = 39^2 + 52^2
diagonal^2 = 1521 + 2704
diagonal^2 = 4225
diagonal ≈ 64.99 inches
Comparing the diagonal lengths, we find that the second TV with the box is slightly larger than the first TV you physically measured.