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)
48+5=53 27+3=30
the square root of 53^2+32^2
61.91 is diagonal
If the TV is 3” wider and 5” higher, what is the new diagonal measurement? (Show work)
48+3=51 27+5=32
the square root of 51^2+32^2
60.21 is diagonal
Depending on the previous responses, why are the diagonal measurements the same or different?
I need help I don't understand the last question
a square has the maximum diagonal for a given perimeter
The first adjustment makes it closer to square, so its diagonal will be greater
Well, let me explain it to you in a funny way. Imagine the TV as a slice of pizza. Now, if you make the pizza 5 inches wider and 3 inches higher, you're basically stretching the dough. But guess what? The amount of cheese and toppings on the pizza stays the same! So, when you take a bigger bite out of the stretched pizza, it looks a bit larger, right? That's why the diagonal measurement increases.
On the other hand, if you make the pizza 3 inches wider and 5 inches higher, you're stretching it in a different direction. This time, you're making the crust bigger, but the cheese and toppings remain the same. So, when you take another bite from the differently stretched pizza, you might think it's a little smaller because your mouth is focusing on the toppings rather than the crust. That's why the diagonal measurement decreases.
In short, depending on how you stretch the pizza, the size of the bite you take will either increase or decrease. It's the same with the TV and its diagonal measurement.
The diagonal measurements are different in the two scenarios because the width and height dimensions change. The diagonal measurement is calculated using the Pythagorean theorem, which states that the square of the diagonal length is equal to the sum of the squares of the width and height lengths. Therefore, when the width and height dimensions change, it affects the overall diagonal measurement.
The last question is asking why the diagonal measurements of the TV are the same or different when it is made wider or taller.
To answer this question, we need to understand how the diagonal measurement of a TV is calculated. The diagonal measurement is the hypotenuse of a right triangle formed by the width, height, and diagonal of the TV screen.
When the TV is made 5 inches wider and 3 inches higher, we can calculate the new diagonal measurement by using the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
So, for the first question, we add 5 to the original width of 48 inches and 3 to the original height of 27 inches. This gives us a new width of 53 inches and a new height of 30 inches. We can then calculate the square of each side (53^2 + 30^2) and find the square root of the sum. This results in a new diagonal measurement of 61.91 inches.
For the second question, when the TV is made 3 inches wider and 5 inches higher, we add 3 to the original width of 48 inches and 5 to the original height of 27 inches. This gives us a new width of 51 inches and a new height of 32 inches. We follow the same steps as before to calculate the new diagonal measurement and find that it is 60.21 inches.
Therefore, the diagonal measurements are different for these two scenarios because the TVs are being made wider and taller by different amounts. The increase in width and height leads to different length of the hypotenuse (diagonal measurement) in each case.