Anonymous
Oct 20
Your brother wants to design a children's playground. It will have a triangular garden with a circular fence. The garden's two sides will measure fifty meters and seven meters.
The angle between them will be forty five degree your brother also want to construct circular fence around the garden such that inside fence perfectly touch the three vertices of the traingular garden your brother intends to put pavers in the region outside the traingular garden but inside the circular fence, each square metres of pavers cost 35000$h , help your brother to identify the type of traingle represented by the triangular garden, coming out with accurate design of the playground
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ChatGPT
Oct 20
To design the children's playground with a triangular garden and circular fence, your brother can follow these steps:
1. Determine the dimensions of the triangular garden:
- The two sides of the triangular garden are given as 50 meters and 7 meters.
- The third side of the triangle can be calculated using the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the two given sides and c is the unknown side.
- In this case, a = 50 meters and b = 7 meters. So, c^2 = 50^2 + 7^2 = 2500 + 49 = 2549.
- Taking the square root of 2549 gives the length of the third side of the triangle, which is approximately 50.49 meters.
2. Calculate the perimeter of the triangular garden:
- The perimeter of a triangle is the sum of its three sides. In this case, the perimeter is 50 + 7 + 50.49 = 107.49 meters.
3. Design the circular fence around the triangular garden:
- The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle.
- The radius of the circular fence should be equal to the perimeter of the triangular garden divided by 2π: r = 107.49 / (2 * π) ≈ 17.13 meters.
- Therefore, the circular fence should have a radius of approximately 17.13 meters.
By following these steps, your brother can design a children's playground with a triangular garden and a circular fence that meets the given dimensions.
1. Determine the dimensions of the triangular garden:
- The two sides of the triangular garden are given as 50 meters and 7 meters.
- The third side of the triangle can be calculated using the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the two given sides and c is the unknown side.
- In this case, a = 50 meters and b = 7 meters. So, c^2 = 50^2 + 7^2 = 2500 + 49 = 2549.
- Taking the square root of 2549 gives the length of the third side of the triangle, which is approximately 50.49 meters.
2. Calculate the perimeter of the triangular garden:
- The perimeter of a triangle is the sum of its three sides. In this case, the perimeter is 50 + 7 + 50.49 = 107.49 meters.
3. Design the circular fence around the triangular garden:
- The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle.
- The radius of the circular fence should be equal to the perimeter of the triangular garden divided by 2π: r = 107.49 / (2 * π) ≈ 17.13 meters.
- Therefore, the circular fence should have a radius of approximately 17.13 meters.
By following these steps, your brother can design a children's playground with a triangular garden and a circular fence that meets the given dimensions.
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Google Gemini AI
Oct 20
The provided information is incomplete. The length of the third side of the triangular garden is missing to calculate the perimeter and determine the radius of the circular fence.
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