do my see what you know about math assignment Some of the great architectural wonders began as mathematical drawings. Mathematical drawings are used by architects, community planners, builders, and landscapers, to name a few. As you work through this task, you will use mathematical drawings to apply your knowledge of the Pythagorean theorem and irrational numbers to develop landscaping plans and to help plan events for the Chicago Park District.
As you complete the task, keep these questions in mind: How can you use the Pythagorean theorem to determine the length of the garden walk at Millennium Park in Chicago? How are irrational numbers used in building a garden walkway?
Directions:
Complete each of the following tasks, reading the directions carefully as you go.
You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all of your work and to answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations.
Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy.
Now let’s get started!
The members of the gardening group plan to build a walkway through the garden as formed by the hypotenuse of each of the four triangles in the drawing. That way, the gardeners will be able to access all sections of the garden. Calculate the length of the entire walkway to the nearest hundredth of a yard. Show your work. (4 points—1 point for each length calculation and 1 point for the total distance)
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⦁ Is the value you just wrote for the total length of the walkway a rational or irrational number? Explain. (2 points)
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⦁ The group is planning to build a fence around the garden. How many yards of fencing materials do they need for the fence? Show your work. (3 points—2 points for finding the value of side b and 1 point for finding the perimeter of the garden)
To complete this task, we need to use the Pythagorean theorem to calculate the lengths of the sides of each triangle and then add them up to find the total length of the walkway.
Given that the lengths of the two shorter sides of the triangles are 3 yards and 4 yards, we can use the Pythagorean theorem to find the length of the hypotenuse of each triangle.
For the first triangle:
a^2 + 3^2 = c^2
a^2 + 9 = c^2
a^2 = c^2 - 9
For the second triangle:
b^2 + 4^2 = c^2
b^2 + 16 = c^2
b^2 = c^2 - 16
For the third triangle:
a^2 + 3^2 = c^2
a^2 + 9 = c^2
a^2 = c^2 - 9
For the fourth triangle:
b^2 + 4^2 = c^2
b^2 + 16 = c^2
b^2 = c^2 - 16
Next, we calculate the value of side a and side b:
For side a:
a = sqrt(c^2 - 9)
a = sqrt(13)
a ≈ 3.61 yards
For side b:
b = sqrt(c^2 - 16)
b = sqrt(13)
b ≈ 3.61 yards
Now, we find the total length of the walkway by adding up the lengths of the four hypotenuses:
Total length = 3.61 + 5 + 3.61 + 5
Total length ≈ 17.22 yards
The value we found for the total length of the walkway is a rational number because it can be expressed as a fraction.
Next, to calculate the perimeter of the garden, we add up the lengths of all four sides:
Perimeter = 3 + 4 + 3 + 4
Perimeter = 14 yards
Therefore, the group needs 14 yards of fencing materials for the fence.