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.
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.
3. Are your measurements the same or different from questions 1 and 2? Explain your answer using
complete sentences.
answer all pls
1. To find the new diagonal measurement, we can use the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) of a right-angled triangle is equal to the sum of the squares of the other two sides.
With the original dimensions of 3 inches wide and 5 inches tall, the diagonal can be calculated as:
Diagonal = √(3^2 + 5^2) = √(9 + 25) = √34 ≈ 5.83 inches
If the new phone is 2 inches wider and 1 inch taller, the new dimensions would be 5 inches wide (3 + 2) and 6 inches tall (5 + 1). Using the same formula:
New diagonal = √(5^2 + 6^2) = √(25 + 36) = √61 ≈ 7.81 inches
Therefore, the new diagonal measurement would be approximately 7.81 inches.
2. If the new phone is 1 inch wider and 2 inches taller, the new dimensions would be 4 inches wide (3 + 1) and 7 inches tall (5 + 2). Using the same formula:
New diagonal = √(4^2 + 7^2) = √(16 + 49) = √65 ≈ 8.06 inches
Therefore, the new diagonal measurement would be approximately 8.06 inches.
3. The measurements from questions 1 and 2 are different. In question 1, the increase in width is greater than the increase in height, resulting in a smaller change in diagonal measurement compared to question 2, where the increase in height is greater than the increase in width. This means that changes in different dimensions of the phone have varying effects on the overall diagonal length.