To find the new diagonal measurement of the TV, we can use the Pythagorean theorem.
Let's call the original width "w", the original height "h", and the original diagonal "d".
According to the given information, we have:
w = 48"
h = 27"
d = 55"
Using the Pythagorean theorem, we can calculate the original diagonal as:
d^2 = w^2 + h^2
55^2 = 48^2 + 27^2
3025 = 2304 + 729
3025 = 3033
Now, let's calculate the new diagonal. Let's call the new width "w2", new height "h2", and the new diagonal "d2".
According to the given information, the TV is 5" wider and 3" higher after the change. So, we have:
w2 = w + 5 = 48 + 5 = 53"
h2 = h + 3 = 27 + 3 = 30"
Again, using the Pythagorean theorem, we can calculate the new diagonal as:
d2^2 = w2^2 + h2^2
d2^2 = 53^2 + 30^2
d2^2 = 2809 + 900
d2^2 = 3709
Taking the square root on both sides, we find:
d2 = √3709 ≈ 60.89"
Therefore, the new diagonal measurement of the TV is approximately 60.89" after it is 5" wider and 3" higher.
If a TV has the following dimensions 48” wide, 27” height, and 55” diagonal. Respond to the following questions.
• If the TV is 5” wider and 3” higher, what is the new diagonal measurement? (Show work)
7 answers
If a TV has the following dimensions 48” wide, 27” height, and 55” diagonal. Respond to the following questions.
• If the TV is 3” wider and 5” 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)
To find the new diagonal measurement of the TV, we can use the Pythagorean theorem.
Let's call the original width "w", the original height "h", and the original diagonal "d".
According to the given information, we have:
w = 48"
h = 27"
d = 55"
Using the Pythagorean theorem, we can calculate the original diagonal as:
d^2 = w^2 + h^2
55^2 = 48^2 + 27^2
3025 = 2304 + 729
3025 = 3033
Now, let's calculate the new diagonal. Let's call the new width "w2", new height "h2", and the new diagonal "d2".
According to the given information, the TV is 3" wider and 5" higher after the change. So, we have:
w2 = w + 3 = 48 + 3 = 51"
h2 = h + 5 = 27 + 5 = 32"
Again, using the Pythagorean theorem, we can calculate the new diagonal as:
d2^2 = w2^2 + h2^2
d2^2 = 51^2 + 32^2
d2^2 = 2601 + 1024
d2^2 = 3625
Taking the square root on both sides, we find:
d2 = √3625 ≈ 60.25"
Therefore, the new diagonal measurement of the TV is approximately 60.25" after it is 3" wider and 5" higher.
Let's call the original width "w", the original height "h", and the original diagonal "d".
According to the given information, we have:
w = 48"
h = 27"
d = 55"
Using the Pythagorean theorem, we can calculate the original diagonal as:
d^2 = w^2 + h^2
55^2 = 48^2 + 27^2
3025 = 2304 + 729
3025 = 3033
Now, let's calculate the new diagonal. Let's call the new width "w2", new height "h2", and the new diagonal "d2".
According to the given information, the TV is 3" wider and 5" higher after the change. So, we have:
w2 = w + 3 = 48 + 3 = 51"
h2 = h + 5 = 27 + 5 = 32"
Again, using the Pythagorean theorem, we can calculate the new diagonal as:
d2^2 = w2^2 + h2^2
d2^2 = 51^2 + 32^2
d2^2 = 2601 + 1024
d2^2 = 3625
Taking the square root on both sides, we find:
d2 = √3625 ≈ 60.25"
Therefore, the new diagonal measurement of the TV is approximately 60.25" after it is 3" wider and 5" higher.
Depending on the previous responses, why are the diagonal measurements the same or different?
The diagonal measurements are different because the dimensions of the TV have changed. In the first response, when the TV is 5" wider and 3" higher, the new diagonal measurement is approximately 60.89". In the second response, when the TV is 3" wider and 5" higher, the new diagonal measurement is approximately 60.25". Since the dimensions of the TV have changed in each scenario, the diagonal measurements are different.
are you sure your answers were correct?
Apologies for the confusion in my previous responses. Let's recalculate the new diagonal measurement correctly this time.
According to the given information, the original width (w) is 48", the original height (h) is 27", and the original diagonal (d) is 55".
Using the Pythagorean theorem, we can calculate the original diagonal as:
d^2 = w^2 + h^2
55^2 = 48^2 + 27^2
3025 = 2304 + 729
3025 = 3033
Now, let's calculate the new diagonal. Let's call the new width "w2", the new height "h2", and the new diagonal "d2".
According to the given information, the TV is 3" wider and 5" higher after the change. So, we have:
w2 = w + 3 = 48 + 3 = 51"
h2 = h + 5 = 27 + 5 = 32".
Again, using the Pythagorean theorem, we can calculate the new diagonal as:
d2^2 = w2^2 + h2^2
d2^2 = 51^2 + 32^2
d2^2 = 2601 + 1024
d2^2 = 3625
Taking the square root on both sides, we find:
d2 = √3625 ≈ 60.21"
Therefore, the correct new diagonal measurement of the TV, when it is 3" wider and 5" higher, is approximately 60.21".
According to the given information, the original width (w) is 48", the original height (h) is 27", and the original diagonal (d) is 55".
Using the Pythagorean theorem, we can calculate the original diagonal as:
d^2 = w^2 + h^2
55^2 = 48^2 + 27^2
3025 = 2304 + 729
3025 = 3033
Now, let's calculate the new diagonal. Let's call the new width "w2", the new height "h2", and the new diagonal "d2".
According to the given information, the TV is 3" wider and 5" higher after the change. So, we have:
w2 = w + 3 = 48 + 3 = 51"
h2 = h + 5 = 27 + 5 = 32".
Again, using the Pythagorean theorem, we can calculate the new diagonal as:
d2^2 = w2^2 + h2^2
d2^2 = 51^2 + 32^2
d2^2 = 2601 + 1024
d2^2 = 3625
Taking the square root on both sides, we find:
d2 = √3625 ≈ 60.21"
Therefore, the correct new diagonal measurement of the TV, when it is 3" wider and 5" higher, is approximately 60.21".
2 answers