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)
If the TV is 3” wider and 5” higher, what is the new diagonal measurement? (Show work)
Depending on the previous responses, why are the diagonal measurements the same or different?
To find the new diagonal measurement, we can use the Pythagorean theorem. According to the theorem, the square of the diagonal is equal to the sum of the squares of the width and height of a right triangle.
For the first question, if the TV is 5 inches wider and 3 inches higher, the new width would be 48 + 5 = 53 inches, and the new height would be 27 + 3 = 30 inches.
Using the Pythagorean theorem, the square of the new diagonal measurement (d1) can be calculated as follows:
d1^2 = 53^2 + 30^2
d1^2 = 2809 + 900
d1^2 = 3709
Taking the square root of both sides, we find that d1 is approximately 60.95 inches.
For the second question, if the TV is 3 inches wider and 5 inches higher, the new width would be 48 + 3 = 51 inches, and the new height would be 27 + 5 = 32 inches.
Using the Pythagorean theorem, the square of the new diagonal measurement (d2) can be calculated as follows:
d2^2 = 51^2 + 32^2
d2^2 = 2601 + 1024
d2^2 = 3625
Taking the square root of both sides, we find that d2 is approximately 60.20 inches.
Comparing the two results, we can see that the new diagonal measurements are slightly different. The first diagonal measurement (d1) is approximately 60.95 inches, while the second diagonal measurement (d2) is approximately 60.20 inches.
The reason for the difference in diagonal measurements is due to the different changes in width and height. Even though both changes increase the overall size of the TV, the change in width has a greater impact on the diagonal measurement compared to the change in height.