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: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.
To find the new diagonal measurement, we can use the Pythagorean theorem as the diagonal forms the hypotenuse of a right triangle.
Let's denote the new width as W and the new height as H.
Given:
Current width: 3 inches
Current height: 5 inches
New width: 3 + 1 = 4 inches
New height: 5 + 2 = 7 inches
Using the Pythagorean theorem, we have:
Diagonal^2 = Width^2 + Height^2
New diagonal^2 = (4 inches)^2 + (7 inches)^2
New diagonal^2 = 16 inches^2 + 49 inches^2
New diagonal^2 = 256 inches^2 + 2401 inches^2
New diagonal^2 = 2657 inches^2
Taking the square root of both sides to solve for the new diagonal:
New diagonal ≈ √2657 inches ≈ 51.55 inches (rounded to the nearest hundredth)
Therefore, the new diagonal measurement of the Samsung Galaxy S23, with 1 inch wider and 2 inches taller dimensions, is approximately 51.55 inches.