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Difficulty: EasyPythagorean Theorem and Special Right Triangles

A rectangular park measures 88 meters in width and 1515 meters in length. A straight walking path extends diagonally across the park from one corner to the opposite corner. What is the length, in meters, of the path?

  1. A
    2323
  2. 1717Answer
  3. C
    289289
  4. D
    161161
  5. E
    23\sqrt{23}

Answer

17 meters
The diagonal of a rectangle forms a right triangle where the width (88 m) and length (1515 m) are legs, and the diagonal path is the hypotenuse. Applying the Pythagorean theorem: d=82+152=64+225=289=17d = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 meters.

Step-by-Step Solution

1
Identify the geometric model and given dimensions
The park is a rectangle with perpendicular sides of length 88 meters and 1515 meters. The diagonal forms a right-angled triangle with these two sides as legs.
Adjacent sides of a rectangle meet at right angles (90∘90^\circ).
2
Apply the Pythagorean theorem to calculate the diagonal length dd
d2=82+152=64+225=289d^2 = 8^2 + 15^2 = 64 + 225 = 289
In any right triangle, the square of the hypotenuse equals the sum of the squares of the legs (a2+b2=c2a^2 + b^2 = c^2).
3
Solve for dd by taking the square root
d=289=17d = \sqrt{289} = 17
The distance dd must be positive.

Key Concept

Pythagorean Theorem (a2+b2=c2a^2 + b^2 = c^2) and the 8−15−178-15-17 Pythagorean Triple
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Topics

Pythagorean Theorem and Special Right Triangles

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