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Pythagorean 2D

Grade 8 · Trigonometry · Worksheet 2

  1. Emma is designing a kite for a school project. The kite has a rectangular frame with a length of 60 cm and a width of 80 cm. She wants to add a diagonal cross-brace for stability. What is the length of this diagonal cross-brace in centimeters?
    Answer: ______________
  2. Mere is constructing a rectangular garden for a community project. The garden has a length of 18 meters and a width of 24 meters. She wants to install a diagonal irrigation pipe from one corner to the opposite corner. What is the length of the diagonal pipe, in meters?
    Answer: ______________
  3. Emma is designing a kite for a school project. The kite has a rectangular frame with a length of 24 inches and a width of 10 inches. She wants to add a diagonal cross-brace for stability. What is the length, in inches, of this diagonal brace? Round your answer to the nearest tenth of an inch.
    Answer: ______________
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Answer Key & Explanations

Pythagorean 2D · Grade 8 · Worksheet 2

  1. Emma is designing a kite for a school project. The kite has a rectangular frame with a length of 60 cm and a width of 80 cm. She wants to add a diagonal cross-brace for stability. What is the length of this diagonal cross-brace in centimeters? Answer: 100 Solution: The diagonal of a rectangle creates a right triangle with the length and width as the two legs. Use the Pythagorean theorem: a² + b² = c², where a and b are the legs and c is the diagonal.
    Full step-by-step solution

    Step 1: The diagonal of a rectangle creates a right triangle with the length and width as the two legs. Step 2: Use the Pythagorean theorem: a² + b² = c², where a and b are the legs and c is the diagonal. Step 3: Substitute the values: 60² + 80² = c² Step 4: Calculate: 3600 + 6400 = c² Step 5: Add: 10000 = c² Step 6: Take the square root: c = sqrt(10000) = 100 Step 7: The diagonal cross-brace is 100 cm long.

  2. Mere is constructing a rectangular garden for a community project. The garden has a length of 18 meters and a width of 24 meters. She wants to install a diagonal irrigation pipe from one corner to the opposite corner. What is the length of the diagonal pipe, in meters? Answer: 30 Solution: The garden forms a right triangle with legs of 18 meters and 24 meters. Let a = 18, b = 24, and c be the diagonal (hypotenuse).
    Full step-by-step solution

    Step 1: The garden forms a right triangle with legs of 18 meters and 24 meters. Step 2: Let a = 18, b = 24, and c be the diagonal (hypotenuse). Step 3: Apply the Pythagorean theorem: a² + b² = c² Step 4: Substitute: 18² + 24² = c² Step 5: Calculate: 324 + 576 = c² Step 6: Add: 900 = c² Step 7: Take the square root: c = sqrt(900) = 30 The diagonal pipe is 30 meters long.

  3. Emma is designing a kite for a school project. The kite has a rectangular frame with a length of 24 inches and a width of 10 inches. She wants to add a diagonal cross-brace for stability. What is the length, in inches, of this diagonal brace? Round your answer to the nearest tenth of an inch. Answer: 26.0 Solution: The diagonal of a rectangle forms a right triangle with the length and width as the two legs. Substitute the known values: 24^2 + 10^2 = c^2 Calculate the squares: 576 + 100 = c^2 Add the results: 676 = c^2 Take the square root of both sides: c = sqrt(676) Calculate the square root: c = 26 The…
    Full step-by-step solution

    Step 1: The diagonal of a rectangle forms a right triangle with the length and width as the two legs. Step 2: Apply the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the sides of the rectangle, and c is the diagonal. Step 3: Substitute the known values: 24^2 + 10^2 = c^2 Step 4: Calculate the squares: 576 + 100 = c^2 Step 5: Add the results: 676 = c^2 Step 6: Take the square root of both sides: c = sqrt(676) Step 7: Calculate the square root: c = 26 Step 8: The problem asks for the answer rounded to the nearest tenth, so 26.0 The length of the diagonal brace is 26.0 inches.