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.
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:
To find the new diagonal measurement, we can use Pythagoras' theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Using the dimensions provided, the original diagonal measurement can be found using the formula:
diagonal^2 = width^2 + height^2
diagonal^2 = 3^2 + 5^2
diagonal^2 = 9 + 25
diagonal^2 = 34
Taking the square root of both sides, we find:
diagonal ≈ √34
Therefore, the original diagonal measurement is approximately 5.83 inches.
If the new phone is 1 inch wider and 2 inches taller, the new dimensions would be:
Width = 3 + 1 = 4 inches
Height = 5 + 2 = 7 inches
Using the same formula, we can find the new diagonal measurement:
diagonal^2 = width^2 + height^2
diagonal^2 = 4^2 + 7^2
diagonal^2 = 16 + 49
diagonal^2 = 65
Taking the square root of both sides, we find:
diagonal ≈ √65
Therefore, the new diagonal measurement is approximately 8.06 inches.
Are your measurements the same or different from questions 1 and 2? Explain your answer using complete sentences.
Bot?
To find the new diagonal measurement of the phone after making it 1 inch wider and 2 inches taller, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the width and height of the phone form a right-angled triangle with the diagonal as the hypotenuse.
The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
where c represents the hypotenuse (diagonal), and a and b represent the other two sides (width and height).
Let's calculate the new diagonal measurement:
Original width (a) = 3 inches
Original height (b) = 5 inches
New width (a') = original width (a) + increase in width (1 inch) = 3 + 1 = 4 inches
New height (b') = original height (b) + increase in height (2 inches) = 5 + 2 = 7 inches
Using the Pythagorean theorem,
New diagonal (c') = sqrt(a'^2 + b'^2)
= sqrt(4^2 + 7^2)
= sqrt(16 + 49)
= sqrt(65)
≈ 8.06 inches
Therefore, the new diagonal measurement of the phone, rounded to the nearest hundredth, is approximately 8.06 inches.