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A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is 2424 meters and the distance between the gopher's holes is 2626 meters. How wide is the yard?\newline___\_\_\_ meters

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Full solution

Q. A gopher has dug holes in opposite corners of a rectangular yard. One length of the yard is 2424 meters and the distance between the gopher's holes is 2626 meters. How wide is the yard?\newline___\_\_\_ meters
  1. Identify Relationship: Identify the relationship between the lengths of the yard and the diagonal using the Pythagorean Theorem.
  2. Define Yard Dimensions: Let the width of the yard be ww meters. The length is 2424 meters, and the diagonal is 2626 meters.
  3. Apply Pythagorean Theorem: Apply the Pythagorean Theorem: w2+242=262 w^2 + 24^2 = 26^2 .
  4. Calculate Squares: Calculate the squares: w2+576=676 w^2 + 576 = 676 .
  5. Subtract to Solve: Subtract 576576 from both sides to solve for w2 w^2 : w2=676−576 w^2 = 676 - 576 .
  6. Calculate Difference: Calculate the difference: w2=100 w^2 = 100 .
  7. Find Width: Take the square root of both sides to find 'w': w=100 w = \sqrt{100} .
  8. Calculate Square Root: Calculate the square root: w=10 w = 10 .

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