Pythagorean Theorem Extended Time
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A boat left a dock and sailed 16 miles north and then sailed 16 miles east, as shown in the diagram at the right. Which of the following is a true statement about the shortest distance the boat must sail to return to the dock?
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The shortest distance back to the dock is 16 miles.
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The shortest distance back to the dock is between 21 and 22 miles.
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The shortest distance back to the dock is between 22 and 23 miles.
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The shortest distance back to the dock is approximately 32 miles.
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Explore the application of the Pythagorean Theorem through practical scenarios in 'Pythagorean Theorem Extended Time'. This quiz assesses understanding of geometric principles in everyday contexts, measuring skills in calculating distances and dimensions effectively.
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The drawing below shows a garden walkway with a triangular flower bed on either side. What is the approximate length of the walkway?
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21.2 feet
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30 feet
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42.4 feet
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450 feet
Correct Answer
A. 21.2 feetExplanation
The approximate length of the walkway is 21.2 feet because it is the only option provided that matches the given answer.Rate this question:
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- 3.
Pat is sewing a rectangular tablecloth for her dining room table. The tablecloth measures 90 cm by 180 cm. She wants to sew a piece of decorative ribbon along both diagonals of the tablecloth. About how much ribbon will she need?
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About 201 cm
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About 402 cm
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About 270 cm
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About 540 cm
Correct Answer
A. About 402 cmExplanation
To find out how much ribbon Pat will need, we can calculate the length of both diagonals of the tablecloth. The length of a diagonal can be found using the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides. In this case, the diagonal is the hypotenuse, and the sides are the length and width of the tablecloth. By applying the theorem, we find that the length of each diagonal is approximately 201 cm. Since Pat wants to sew ribbon along both diagonals, she will need a total of approximately 402 cm of ribbon.Rate this question:
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- 4.
A television screen is described in terms of the diagonal measure of its screen. If a TV screen is 20 inches wide and 15 inches high, what is the length of its diagonal?
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5.9 inches
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13.2 inches
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25 inches
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625 inches
Correct Answer
A. 25 inchesExplanation
The length of the diagonal of a rectangle can be found using the Pythagorean theorem. In this case, the width is 20 inches and the height is 15 inches. Using the theorem, we can calculate the diagonal as follows: diagonal = √(width^2 + height^2) = √(20^2 + 15^2) = √(400 + 225) = √625 = 25 inches. Therefore, the correct answer is 25 inches.Rate this question:
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- 5.
Mr. Elliott designed a flower garden in the shape of a square. He plans to build a walkway through the garden, as shown below. Which is the closet to the length of the walkway?
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36 ft
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24 ft
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17 ft
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13 ft
Correct Answer
A. 17 ftExplanation
The walkway is going to be the diagonal of the square garden. In a square, the length of the diagonal can be found using the Pythagorean theorem, which states that the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides. Since the sides of the square garden are all equal, we can say that the length of the diagonal is equal to the square root of 2 times the length of the side. In this case, the length of the side is 12 ft, so the length of the diagonal (walkway) is approximately 17 ft.Rate this question:
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- 6.
Kari lives 5 miles due east of Jack, and Ryan lives 8 miles due north of Kari. What is the approximate distance from Jack’s house to Ryan’s house?
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6.2 miles
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9.4 miles
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8.9 miles
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13.1
Correct Answer
A. 9.4 milesExplanation
Kari lives 5 miles due east of Jack, and Ryan lives 8 miles due north of Kari. To find the approximate distance from Jack's house to Ryan's house, we can use the Pythagorean theorem. The distance between Jack and Kari can be considered as the base of a right triangle, and the distance between Kari and Ryan can be considered as the height of the right triangle. By using the Pythagorean theorem, we can calculate the hypotenuse, which represents the approximate distance from Jack's house to Ryan's house. The calculation is √(5^2 + 8^2) = √(25 + 64) = √89 ≈ 9.4 miles.Rate this question:
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.png "The drawing below shows a garden walkway with a triangular flower bed on either side.
What is the approximate length of the walkway?")
.png "Pat is sewing a rectangular tablecloth for her dining room table. The tablecloth measures 90 cm by 180 cm. She wants to sew a piece of decorative ribbon along both diagonals of the tablecloth.
About how much ribbon will she need?")
.png "Mr. Elliott designed a flower garden in the shape of a square. He plans to build a walkway through the garden, as shown below.
Which is the closet to the length of the walkway?")
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Current Version
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Mar 21, 2023Quiz Edited by
ProProfs Editorial Team -
May 08, 2013Quiz Created by
Lesliedulock
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