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Difficulty: MediumPerimeter and Area of 2D Figures

A rectangular swimming pool is twice as long as it is wide. It is surrounded by a tiled deck that has a uniform width of 22 meters. If the area of the deck alone is 136136 square meters, what is the perimeter of the swimming pool in meters?

  1. A
    50
  2. 60Answer
  3. C
    132
  4. D
    200

Answer

60
The correct answer accurately models the outer dimensions of the pool plus deck as (w+4)(w + 4) and (2w+4)(2w + 4). Subtracting the inner pool area (2w2)(2w^2) leaves the deck area equation 12w+16=13612w + 16 = 136. Solving this yields a width of 1010 meters and a length of 2020 meters, giving a perimeter of 6060 meters.

Step-by-Step Solution

1
Define variables for the dimensions of the pool and the outer boundaries including the deck.
Let width = ww and length = 2w2w. The outer dimensions, which add the 2-meter deck to both sides, are width = w+4w + 4 and length = 2w+42w + 4.
This establishes algebraic expressions to represent the areas.
2
Set up an equation for the deck area by subtracting the pool's area from the total outer area.
(w+4)(2w+4)−(w)(2w)=136(w + 4)(2w + 4) - (w)(2w) = 136
The area of the deck alone is given as 136 square meters.
3
Expand the expressions and solve the equation for ww.
(2w2+12w+16)−2w2=136→12w+16=136→12w=120→w=10(2w^2 + 12w + 16) - 2w^2 = 136 \rightarrow 12w + 16 = 136 \rightarrow 12w = 120 \rightarrow w = 10 meters.
Simplifying isolates the variable ww to find the width of the pool.
4
Calculate the pool's length and then its perimeter.
Length = 2(10)=202(10) = 20 meters. Perimeter = 2(10+20)=602(10 + 20) = 60 meters.
The question asks for the perimeter of the swimming pool.

Key Concept

Solving for unknown geometric dimensions using the area of a surrounding path, followed by perimeter calculation.
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Topics

Perimeter and Area of 2D Figures

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