Task 2 (6 pts): 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)
Work done on a separate sheet of paper
ANSWER: 48”
If the TV is 3” wider and 5” higher, what is the new diagonal measurement? (Show work)
Work done on a separate sheet of paper
ANSWER: 55”
Depending on the previous responses, why are the diagonal measurements the same or different?
**this is what i have so far- can someone help me please***
To find the new diagonal measurement, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides.
Let's first find the original diagonal measurement using the given dimensions: width = 48" and height = 27".
Using the Pythagorean theorem, we can calculate the original diagonal as follows:
Diagonal^2 = Width^2 + Height^2
Diagonal^2 = 48^2 + 27^2
Diagonal^2 = 2304 + 729
Diagonal^2 = 3033
Diagonal ≈ square root of 3033
Diagonal ≈ 55" (rounded to the nearest whole number)
Now, let's consider the first scenario where the TV is 5" wider and 3" higher. We can calculate the new diagonal measurement using the same method as before:
Width = Original width + Increase in width = 48" + 5" = 53"
Height = Original height + Increase in height = 27" + 3" = 30"
Diagonal^2 = Width^2 + Height^2
Diagonal^2 = 53^2 + 30^2
Diagonal^2 = 2809 + 900
Diagonal^2 = 3709
Diagonal ≈ square root of 3709
Diagonal ≈ 60" (rounded to the nearest whole number)
In the second scenario where the TV is 3" wider and 5" higher, we can calculate the new diagonal measurement as follows:
Width = Original width + Increase in width = 48" + 3" = 51"
Height = Original height + Increase in height = 27" + 5" = 32"
Diagonal^2 = Width^2 + Height^2
Diagonal^2 = 51^2 + 32^2
Diagonal^2 = 2601 + 1024
Diagonal^2 = 3625
Diagonal ≈ square root of 3625
Diagonal ≈ 60" (rounded to the nearest whole number)
From the calculations, we can see that in both scenarios, the new diagonal measurements are the same (60"). This happens because the increase in width and height is proportional, maintaining the same aspect ratio. As a result, the new diagonals end up being equal.