If a TV has the following dimensions 48” wide, 27” height, and 55” diagonal. Respond to the following questions.

Question

• If the TV is 5” wider and 3” higher, what is the new diagonal measurement? (Show work)

Use the Pythagorean theorem

Answer 1

to find the original diagonal measurement:
diagonal^2 = width^2 + height^2
diagonal^2 = 48^2 + 27^2
diagonal^2 = 2304 + 729
diagonal^2 = 3033
diagonal ≈ 55.08

To find the new diagonal measurement:
new_diagonal^2 = (width + 5)^2 + (height + 3)^2
new_diagonal^2 = (48 + 5)^2 + (27 + 3)^2
new_diagonal^2 = 53^2 + 30^2
new_diagonal^2 = 2809 + 900
new_diagonal^2 = 3709
new_diagonal ≈ 60.91

Therefore, the new diagonal measurement is approximately 60.91 inches.

Answer 2

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)

Answer 3

To find the new diagonal measurement, we can use the Pythagorean theorem, which states that the square of the diagonal is equal to the sum of the squares of the width and height.

For the original TV:
Diagonal^2 = Width^2 + Height^2
55^2 = 48^2 + 27^2
3025 = 2304 + 729
3025 = 3033

Taking the square root of both sides, we find:
Diagonal = sqrt(3025)
Diagonal = 55 inches

For the TV that is 5 inches wider and 3 inches higher:
New Width = 48 + 5 = 53 inches
New Height = 27 + 3 = 30 inches

New Diagonal^2 = New Width^2 + New Height^2
New Diagonal^2 = 53^2 + 30^2
New Diagonal^2 = 2809 + 900
New Diagonal^2 = 3709

Taking the square root of both sides, we find:
New Diagonal = sqrt(3709)
New Diagonal ≈ 60.91 inches

Therefore, the new diagonal measurement is approximately 60.91 inches.