Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine the approximate perimeter of a kite with vertices at [tex]\((2, 4)\)[/tex], [tex]\((5, 4)\)[/tex], [tex]\((5, 1)\)[/tex], and [tex]\((0, -1)\)[/tex], we need to calculate the lengths of its four sides and then sum these lengths. Here are the detailed steps:
1. Calculate the distance between the vertices [tex]\((2, 4)\)[/tex] and [tex]\((5, 4)\)[/tex]:
These points share the same y-coordinate, so the distance is simply the difference in x-coordinates:
[tex]\[ \text{Distance} = \sqrt{(5 - 2)^2 + (4 - 4)^2} = \sqrt{3^2 + 0^2} = \sqrt{9} = 3.0 \][/tex]
2. Calculate the distance between the vertices [tex]\((5, 4)\)[/tex] and [tex]\((5, 1)\)[/tex]:
These points share the same x-coordinate, so the distance is simply the difference in y-coordinates:
[tex]\[ \text{Distance} = \sqrt{(5 - 5)^2 + (4 - 1)^2} = \sqrt{0^2 + 3^2} = \sqrt{9} = 3.0 \][/tex]
3. Calculate the distance between the vertices [tex]\((5, 1)\)[/tex] and [tex]\((0, -1)\)[/tex]:
[tex]\[ \text{Distance} = \sqrt{(0 - 5)^2 + (-1 - 1)^2} = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.385 \][/tex]
4. Calculate the distance between the vertices [tex]\((0, -1)\)[/tex] and [tex]\((2, 4)\)[/tex]:
[tex]\[ \text{Distance} = \sqrt{(2 - 0)^2 + (4 - (-1))^2} = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.385 \][/tex]
Next, we add these distances together to find the perimeter of the kite:
[tex]\[ \text{Perimeter} = 3.0 + 3.0 + 5.385 + 5.385 \approx 16.770 \][/tex]
Rounding this to the nearest tenth:
[tex]\[ \text{Perimeter} \approx 16.8 \text{ units} \][/tex]
Thus, the approximate perimeter of the kite is [tex]\(16.8\)[/tex] units. Therefore, the correct answer is:
[tex]\[ \boxed{16.8 \text{ units}} \][/tex]
1. Calculate the distance between the vertices [tex]\((2, 4)\)[/tex] and [tex]\((5, 4)\)[/tex]:
These points share the same y-coordinate, so the distance is simply the difference in x-coordinates:
[tex]\[ \text{Distance} = \sqrt{(5 - 2)^2 + (4 - 4)^2} = \sqrt{3^2 + 0^2} = \sqrt{9} = 3.0 \][/tex]
2. Calculate the distance between the vertices [tex]\((5, 4)\)[/tex] and [tex]\((5, 1)\)[/tex]:
These points share the same x-coordinate, so the distance is simply the difference in y-coordinates:
[tex]\[ \text{Distance} = \sqrt{(5 - 5)^2 + (4 - 1)^2} = \sqrt{0^2 + 3^2} = \sqrt{9} = 3.0 \][/tex]
3. Calculate the distance between the vertices [tex]\((5, 1)\)[/tex] and [tex]\((0, -1)\)[/tex]:
[tex]\[ \text{Distance} = \sqrt{(0 - 5)^2 + (-1 - 1)^2} = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.385 \][/tex]
4. Calculate the distance between the vertices [tex]\((0, -1)\)[/tex] and [tex]\((2, 4)\)[/tex]:
[tex]\[ \text{Distance} = \sqrt{(2 - 0)^2 + (4 - (-1))^2} = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.385 \][/tex]
Next, we add these distances together to find the perimeter of the kite:
[tex]\[ \text{Perimeter} = 3.0 + 3.0 + 5.385 + 5.385 \approx 16.770 \][/tex]
Rounding this to the nearest tenth:
[tex]\[ \text{Perimeter} \approx 16.8 \text{ units} \][/tex]
Thus, the approximate perimeter of the kite is [tex]\(16.8\)[/tex] units. Therefore, the correct answer is:
[tex]\[ \boxed{16.8 \text{ units}} \][/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.