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 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, Answer to question 1: the new diagonal measurement is approximately 36 inches.

Question

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 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, Answer to question 1: the new diagonal measurement is approximately 36 inches.

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. 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, Answer to question 2: the new diagonal measurement is approximately 49 inches.

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

Answer 1

The measurements in questions 1 and 2 are different. In question 1, the new phone was made 2 inches wider and 1 inch taller, resulting in a new diagonal measurement of approximately 36 inches. In question 2, the new phone was made 1 inch wider and 2 inches taller, resulting in a new diagonal measurement of approximately 49 inches. This difference is due to the varying proportions of width and height changes in the two scenarios.