32” TV height: 16” width: _____
• _____ TV height: 34” width: 61”
• 60” TV height: 30” width: _____
• _____ TV height: 20” width: 35”
• 52” TV height: _____ width: 45”
If the TV is 5” wider and 3” higher, what is the new diagonal measurement? (Show work)
If the TV is 3” wider and 5” higher, what is the new diagonal measurement? (Show work)
im confused
width^2 + height^2=diagnonal^2
on the last two, I am not clear what the original height, width were.
someone pls explain how do to this
To solve these questions, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's solve each question step by step:
1. For the given TV with a height of 32” and an unknown width:
We can use the Pythagorean theorem to find the width:
Width^2 + Height^2 = Diagonal^2
Width^2 + 32^2 = Diagonal^2
Since the diagonal is the same as the given height of 32”, we can substitute the values:
Width^2 + 32^2 = 32^2
Width^2 = 32^2 - 32^2
Width^2 = 0
Therefore, the width is 0 inches.
2. For the given TV with a height of 34” and a width of 61”:
We can use the Pythagorean theorem to find the diagonal:
Width^2 + Height^2 = Diagonal^2
61^2 + 34^2 = Diagonal^2
Diagonal^2 = 3721 + 1156
Diagonal^2 = 4877
Diagonal ≈ √4877 ≈ 69.85 inches (rounded to two decimal places)
3. For the given TV with a height of 60” and an unknown width:
Using the Pythagorean theorem, we can find the width:
Width^2 + 60^2 = Diagonal^2
Since the diagonal is not given, we can't find the exact value of the diagonal.
4. For the given TV with a height of 20” and a width of 35”:
Using the Pythagorean theorem, we can find the diagonal:
Width^2 + 20^2 = Diagonal^2
35^2 + 20^2 = Diagonal^2
Diagonal^2 = 1225 + 400
Diagonal^2 = 1625
Diagonal ≈ √1625 ≈ 40.31 inches (rounded to two decimal places)
5. For the given TV with an unknown height and a width of 45”:
We can't find the height without any additional information.
Now let's calculate the new diagonal measurements for both cases:
• If the TV is 5” wider and 3” higher:
For the first case, where the TV is 5 inches wider and 3 inches higher than the original TV with a diagonal of 32”:
Width = 0 + 5 = 5 inches wider than before
Height = 32 + 3 = 35 inches higher than before
Using the Pythagorean theorem:
Width^2 + Height^2 = Diagonal^2
5^2 + 35^2 = Diagonal^2
Diagonal^2 = 25 + 1225
Diagonal^2 = 1250
Diagonal ≈ √1250 ≈ 35.36 inches (rounded to two decimal places)
• If the TV is 3” wider and 5” higher:
For the second case, where the TV is 3 inches wider and 5 inches higher than the original TV with a diagonal of 32”:
Width = 0 + 3 = 3 inches wider than before
Height = 32 + 5 = 37 inches higher than before
Using the Pythagorean theorem:
Width^2 + Height^2 = Diagonal^2
3^2 + 37^2 = Diagonal^2
Diagonal^2 = 9 + 1369
Diagonal^2 = 1378
Diagonal ≈ √1378 ≈ 37.12 inches (rounded to two decimal places)
Therefore, the new diagonal measurements are approximately 35.36 inches and 37.12 inches, respectively, for the two cases.