Samsung Galaxy S23+

The cell phone is Samsung Galaxy S23+ with a height of 5 inches and a width of 3 inches.

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To use the Pythagorean theorem in this context, we can consider the height and width of the Samsung Galaxy S23+ as the legs of a right triangle, and the diagonal of the phone as the hypotenuse.

Let's assume the diagonal of the phone is represented by 'd'.

According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

So, in this case, we have:

(Height)^2 + (Width)^2 = (Diagonal)^2

Substituting the given values, we have:

(5 in.)^2 + (3 in.)^2 = d^2

25 in.^2 + 9 in.^2 = d^2

34 in.^2 = d^2

Taking the square root of both sides, we find:

d = √34 in.

Therefore, the diagonal of the Samsung Galaxy S23+ is approximately √34 inches.

. iPad 3

iPad: _____; Height: 10 in.; Width: 7 in

The iPad model is iPad 3 with a height of 10 inches and a width of 7 inches.

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I believe you meant to refer to the Pythagorean theorem. The Pythagorean theorem is applicable to right triangles, where the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

In the case of the iPad 3, we can consider the height and width of the iPad as the legs of a right triangle, and the diagonal as the hypotenuse. Let's assume the diagonal is represented by 'd'.

According to the Pythagorean theorem, we have:

(Height)^2 + (Width)^2 = (Diagonal)^2

Substituting the given values, we have:

(10 in.)^2 + (7 in.)^2 = d^2

100 in.^2 + 49 in.^2 = d^2

149 in.^2 = d^2

Taking the square root of both sides, we find:

d = √149 in.

Therefore, the diagonal of the iPad 3 is approximately √149 inches.

4. HP Pavillion 15-e000 Series Laptop Laptop: 18 in.; Height: _____; Width: 10 in

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To use the Pythagorean theorem in this context, we can consider the height and width of the HP Pavilion 15-e000 Series laptop as the legs of a right triangle, and the diagonal of the laptop as the hypotenuse. Let's assume the height is represented by 'h'.

According to the Pythagorean theorem, we have:

(Height)^2 + (Width)^2 = (Diagonal)^2

Substituting the given values, we have:

(h)^2 + (10 in.)^2 = (18 in.)^2

h^2 + 100 in.^2 = 324 in.^2

h^2 = 324 in.^2 - 100 in.^2

h^2 = 224 in.^2

Taking the square root of both sides, we find:

h = √224 in.

Therefore, the height of the HP Pavilion 15-e000 Series laptop is approximately √224 inches.

6. Movie Theater Screen

Theater Screen: 76 ft. Height: 30 ft.; Width: ____
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I believe you meant to refer to the Pythagorean theorem. The Pythagorean theorem can be applied in this context by considering the height and width of the movie theater screen as the legs of a right triangle, and the diagonal as the hypotenuse. Let's assume the width is represented by 'w'.

According to the Pythagorean theorem, we have:

(Height)^2 + (Width)^2 = (Diagonal)^2

Substituting the given values, we have:

(30 ft.)^2 + (w)^2 = (76 ft.)^2

900 ft.^2 + w^2 = 5776 ft.^2

w^2 = 5776 ft.^2 - 900 ft.^2

w^2 = 4876 ft.^2

Taking the square root of both sides, we find:

w = √4876 ft.

Therefore, the width of the movie theater screen is approximately √4876 feet.

Chromebook

Chromebook: 14 in; Height: ____; Width: 12 in.
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To use the Pythagorean theorem in this context, we can consider the height and width of the Chromebook as the legs of a right triangle, and the diagonal of the Chromebook as the hypotenuse. Let's assume the height is represented by 'h'.

According to the Pythagorean theorem, we have:

(Height)^2 + (Width)^2 = (Diagonal)^2

Substituting the given values, we have:

(h)^2 + (12 in.)^2 = (14 in.)^2

h^2 + 144 in.^2 = 196 in.^2

h^2 = 196 in.^2 - 144 in.^2

h^2 = 52 in.^2

Taking the square root of both sides, we find:

h = √52 in.

Therefore, the height of the Chromebook is approximately √52 inches.

5. TV in someone’s living room

TV: 57 in; Height: 30 in.; Width: _____
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To use the Pythagorean theorem in this context, we can consider the height and width of the TV as the legs of a right triangle, and the diagonal of the TV as the hypotenuse. Let's assume the width is represented by 'w'.

According to the Pythagorean theorem, we have:

(Height)^2 + (Width)^2 = (Diagonal)^2

Substituting the given values, we have:

(30 in.)^2 + (w)^2 = (57 in.)^2

900 in.^2 + w^2 = 3249 in.^2

w^2 = 3249 in.^2 - 900 in.^2

w^2 = 2349 in.^2

Taking the square root of both sides, we find:

w = √2349 in.

Therefore, the width of the TV in someone's living room is approximately √2349 inches.

6. Movie Theater Screen

Theater Screen: 76 ft. Height: 30 ft.; Width: ____
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To use the Pythagorean theorem in this context, we can consider the height and width of the movie theater screen as the legs of a right triangle, and the diagonal of the screen as the hypotenuse. Let's assume the width is represented by 'w'.

According to the Pythagorean theorem, we have:

(Height)^2 + (Width)^2 = (Diagonal)^2

Substituting the given values, we have:

(30 ft.)^2 + (w)^2 = (76 ft.)^2

900 ft.^2 + w^2 = 5776 ft.^2

w^2 = 5776 ft.^2 - 900 ft.^2

w^2 = 4876 ft.^2

Taking the square root of both sides, we find:

w = √4876 ft.

Therefore, the width of the movie theater screen is approximately √4876 feet.

3 inches wide, 5 inches tall, and 6-inch diagonal. Respond to the following questions:

1. If your team makes the new phone 2 inches wider and 1 inch taller, what is the new diagonal measurement? (Show work). Round your answer to the nearest hundredth.
2. If your team makes the new phone 1 inch wider and 2 inches taller, what is the new diagonal measurement? (Show work). Round your answer to the nearest hundredth.
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To find the new diagonal measurement, we can use the Pythagorean theorem. Let's denote the original width and height as 'w' and 'h' respectively, and the original diagonal measurement as 'd'.

Original measurements:
Width (w) = 3 inches
Height (h) = 5 inches
Diagonal (d) = 6 inches

1. If the new phone is made 2 inches wider and 1 inch taller:
New width = w + 2 inches = 3 + 2 = 5 inches
New height = h + 1 inch = 5 + 1 = 6 inches

Using the Pythagorean theorem:
(New height)^2 + (New width)^2 = (New diagonal)^2
(6 inches)^2 + (5 inches)^2 = (New diagonal)^2
36 inches^2 + 25 inches^2 = (New diagonal)^2
1296 inches^2 = (New diagonal)^2

Taking the square root of both sides:
New diagonal = √1296 inches
New diagonal ≈ 36 inches

Therefore, if the new phone is made 2 inches wider and 1 inch taller, the new diagonal measurement is approximately 36 inches.

2. If the new phone is made 1 inch wider and 2 inches taller:
New width = w + 1 inch = 3 + 1 = 4 inches
New height = h + 2 inches = 5 + 2 = 7 inches

Using the Pythagorean theorem:
(New height)^2 + (New width)^2 = (New diagonal)^2
(7 inches)^2 + (4 inches)^2 = (New diagonal)^2
49 inches^2 + 16 inches^2 = (New diagonal)^2
2401 inches^2 = (New diagonal)^2

Taking the square root of both sides:
New diagonal = √2401 inches
New diagonal ≈ 49 inches

Therefore, if the new phone is made 1 inch wider and 2 inches taller, the new diagonal measurement is approximately 49 inches.