apply the pythagorem theroem to this question

Question

a2 + b2 = c2
Task 2: Imagine you are on the design team at Samsung. The company has tasked your team with deciding the dimensions for the next cell phone model. The Samsung Galaxy S23 has the following dimensions: 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.

Answer 1

To apply the Pythagorean theorem in this scenario, we can find the original diagonal length using the given dimensions:

a = 3 inches (width)
b = 5 inches (height)
c = 6 inches (diagonal)

Using the Pythagorean theorem equation: a^2 + b^2 = c^2, we can solve for c:

3^2 + 5^2 = c^2
9 + 25 = c^2
34 = c^2
c ≈ √34
c ≈ 5.83 inches (rounded to the nearest hundredth)

Now, to find the new diagonal measurement after increasing the width by 2 inches and the height by 1 inch:

a = 3 + 2 = 5 inches (new width)
b = 5 + 1 = 6 inches (new height)
Using the same Pythagorean theorem equation: a^2 + b^2 = c^2, we can solve for c:

5^2 + 6^2 = c^2
25 + 36 = c^2
61 = c^2
c ≈ √61
c ≈ 7.81 inches (rounded to the nearest hundredth)

Therefore, the new diagonal measurement for the Samsung Galaxy S23 after increasing the width by 2 inches and the height by 1 inch is approximately 7.81 inches.

Answer 2

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.

Answer 3

To find the new diagonal measurement after increasing the width by 1 inch and the height by 2 inches:

a = 3 + 1 = 4 inches (new width)
b = 5 + 2 = 7 inches (new height)
Using the same Pythagorean theorem equation: a^2 + b^2 = c^2, we can solve for c:

4^2 + 7^2 = c^2
16 + 49 = c^2
65 = c^2
c ≈ √65
c ≈ 8.06 inches (rounded to the nearest hundredth)

Therefore, the new diagonal measurement for the Samsung Galaxy S23 after increasing the width by 1 inch and the height by 2 inches is approximately 8.06 inches.

Answer 4

Are your measurements the same or different from questions 1 and 2? Explain your answer using complete sentences.

Answer 5

Are your measurements the same or different from questions 1 and 2? Explain your answer using complete sentences. .

Answer 6

The measurements in questions 1 and 2 are different. In question 1, the team increased the width by 2 inches and the height by 1 inch, resulting in a new diagonal measurement of approximately 7.81 inches. In question 2, the team increased the width by 1 inch and the height by 2 inches, resulting in a new diagonal measurement of approximately 8.06 inches. These measurements are different because the changes in dimensions are not the same in both questions.