Part 1: 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.(5 points)
How large is TV #1? The first TV measures
inches diagonally.
Question 2
Part 2: Now find the diagonal length of TV #2. Which TV is larger and why? You must show all of your work for Part 1 in here as well as your conclusion of Part 2 for full credit. (10 points)
To find the diagonal length of TV #1, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's label the length of TV #1 as A, and the width as B. We know that A = 32 inches and B = 56 inches.
Using the Pythagorean theorem, we can find the diagonal length (C) of TV #1:
C^2 = A^2 + B^2
C^2 = 32^2 + 56^2
C^2 = 1024 + 3136
C^2 = 4160
To find C, we take the square root of both sides:
C = sqrt(4160)
C ≈ 64.49 inches
Therefore, the diagonal length of TV #1 is approximately 64.49 inches.
Now let's find the diagonal length of TV #2. We are given that the length is 39 inches and the width is 52 inches.
Using the same process as above, we find:
C^2 = 39^2 + 52^2
C^2 = 1521 + 2704
C^2 = 4225
Again, taking the square root of both sides:
C = sqrt(4225)
C = 65 inches
Therefore, the diagonal length of TV #2 is 65 inches.
By comparing the diagonal lengths, we can conclude that TV #2 is larger because its diagonal length (65 inches) is greater than the diagonal length of TV #1 (approximately 64.49 inches).
Part 1:
To find out the diagonal length of TV #1, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.
Let's assume the length of TV #1 is "L1" and the width is "W1."
Using the given measurements, L1 = 32 inches and W1 = 56 inches.
To find the diagonal length, D1 (in inches), we can use the formula:
D1^2 = L1^2 + W1^2
Substituting the values, we get:
D1^2 = 32^2 + 56^2
D1^2 = 1024 + 3136
D1^2 = 4160
Taking the square root of both sides, we find:
D1 = √4160
D1 ≈ 64.5 inches
Therefore, TV #1 has a diagonal length of approximately 64.5 inches.
Part 2:
To find the diagonal length of TV #2, we can use the same formula as in Part 1.
Let's assume the length of TV #2 is "L2" and the width is "W2."
From the given information, L2 (in inches) = 39 inches and W2 (in inches) = 52 inches.
Using the formula mentioned earlier, we can calculate the diagonal length D2 (in inches):
D2^2 = L2^2 + W2^2
Substituting the values, we get:
D2^2 = 39^2 + 52^2
D2^2 = 1521 + 2704
D2^2 = 4225
Taking the square root of both sides, we find:
D2 = √4225
D2 = 65 inches
Therefore, TV #2 has a diagonal length of 65 inches.
Conclusion:
TV #2 is larger than TV #1 because it has a greater diagonal length. TV #2 measures 65 inches diagonally, while TV #1 measures approximately 64.5 inches diagonally.
To find the diagonal length of a TV, we can use the Pythagorean theorem. According to the theorem, the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
For TV #1, we are given the length and width. Let's call the length "a" and the width "b". Using the Pythagorean theorem, we can calculate the diagonal length as follows:
Diagonal length^2 = length^2 + width^2
Diagonal length^2 = 32^2 + 56^2
Diagonal length^2 = 1024 + 3136
Diagonal length^2 = 4160
Taking the square root of both sides, we find:
Diagonal length = √4160
Diagonal length ≈ 64.49 inches
So, TV #1 measures approximately 64.49 inches diagonally.
For TV #2, we are given the length and width as well. Let's call the length "c" and the width "d". Using the Pythagorean theorem, we can calculate the diagonal length as follows:
Diagonal length^2 = length^2 + width^2
Diagonal length^2 = 39^2 + 52^2
Diagonal length^2 = 1521 + 2704
Diagonal length^2 = 4225
Taking the square root of both sides, we find:
Diagonal length = √4225
Diagonal length = 65 inches
Therefore, TV #2 measures approximately 65 inches diagonally.
Conclusion:
From our calculations, we can see that TV #2 is larger than TV #1. The diagonal length of TV #2 is 65 inches, whereas the diagonal length of TV #1 is 64.49 inches. So TV #2 is larger by approximately 0.51 inches.