apply the pythagorem theroem to this 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.
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.
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.
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.
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.
Are your measurements the same or different from questions 1 and 2? Explain your answer using complete sentences.
Are your measurements the same or different from questions 1 and 2? Explain your answer using complete sentences. .
To apply the Pythagorean theorem to this question, we can use the formula a^2 + b^2 = c^2, where a and b represent the sides of a right triangle and c represents the hypotenuse (the longest side).
In this case, we need to find the new diagonal measurement after making the Samsung Galaxy S23 model 2 inches wider and 1 inch taller.
Given:
a = 3 inches (width)
b = 5 inches (height)
c = 6 inches (initial diagonal measurement)
To find the new diagonal measurement, let's calculate the new values for a and b and then substitute them into the Pythagorean theorem formula.
New width (a):
3 inches + 2 inches (increase in width) = 5 inches
New height (b):
5 inches + 1 inch (increase in height) = 6 inches
Now, let's substitute the values into the Pythagorean theorem formula:
(5 inches)^2 + (6 inches)^2 = c^2
25 inches^2 + 36 inches^2 = c^2
625 inches^2 + 1296 inches^2 = c^2
1921 inches^2 = c^2
To find c, we need to take the square root of both sides:
√(1921 inches^2) = √(c^2)
43.84 inches = c
Rounding to the nearest hundredth, the new diagonal measurement is approximately 43.84 inches.