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Difficulty: MediumTriangles and Pythagorean Theorem

A rectangular swimming pool has a diagonal length of 20 meters20\text{ meters} and a width of 12 meters12\text{ meters}. What is the perimeter of the swimming pool?

  1. A
    16 meters16\text{ meters}
  2. B
    48 meters48\text{ meters}
  3. 56 meters56\text{ meters}Answer
  4. D
    64 meters64\text{ meters}

Answer

56 meters56\text{ meters}
The diagonal of a rectangle creates a right triangle where the diagonal is the hypotenuse. Using the Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2), the missing length is 202−122=400−144=256=16 meters\sqrt{20^2 - 12^2} = \sqrt{400 - 144} = \sqrt{256} = 16\text{ meters}. The perimeter of the rectangle is the total distance around the outside, which is calculated as 2×(width+length)=2×(12+16)=2×28=56 meters2 \times (\text{width} + \text{length}) = 2 \times (12 + 16) = 2 \times 28 = 56\text{ meters}.

Step-by-Step Solution

1
Identify the geometric relationship between the dimensions.
The width, length, and diagonal of a rectangle form a right triangle where the diagonal is the hypotenuse.
Rectangles have right angles at all corners, allowing the use of the Pythagorean theorem.
2
Use the Pythagorean theorem to find the length of the pool.
122+length2=20212^2 + \text{length}^2 = 20^2, which becomes 144+length2=400144 + \text{length}^2 = 400. Subtracting 144144 gives length2=256\text{length}^2 = 256, so the length is 16 meters16\text{ meters}.
The Pythagorean theorem (a2+b2=c2a^2 + b^2 = c^2) allows us to find a missing side of a right triangle when two sides are known.
3
Calculate the perimeter of the rectangle.
Perimeter = 2×(width+length)=2×(12+16)=2×28=56 meters2 \times (\text{width} + \text{length}) = 2 \times (12 + 16) = 2 \times 28 = 56\text{ meters}.
The question asks for the perimeter of the entire rectangular pool, which requires combining all four outer sides.

Key Concept

Applying the Pythagorean theorem to find missing dimensions before calculating perimeter.
Estimated Time:1m 0s
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Topics

Triangles and Pythagorean Theorem

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