A rectangular swimming pool is 25 meters long and 10 meters wide. If a deck of uniform width surrounds the pool and the total area including the deck is 400 square meters, what is the width of the deck? - RTA
A rectangular swimming pool is 25 meters long and 10 meters wide. If a deck of uniform width surrounds the pool and the total area including the deck is 400 square meters, what is the width of the deck?
A rectangular swimming pool is 25 meters long and 10 meters wide. If a deck of uniform width surrounds the pool and the total area including the deck is 400 square meters, what is the width of the deck?
A rectangular swimming pool measuring 25 meters by 10 meters acts as a familiar centerpiece in many American homes. As pool ownership grows alongside rising interest in outdoor living and home relaxation, more people are exploring ways to enhance these spaces with decks—open areas that blend functionality with style. The query asking for the uniform deck width around such a pool reflects a tangible, real-life planning challenge: maximizing space and aesthetics while managing layout and budget. With a total area of 400 square meters, the calculation reveals how even small changes in surrounding space can significantly impact the final design.
Understanding the Context
Why Is This Question Gaining Traction in the U.S.?
In recent years, mobile-first homeowners across the United States are prioritizing outdoor environments that support family gatherings, casual entertainment, and healthy recreation. The popularity of outdoor furniture, pool maintenance, and home transformation projects has driven curiosity about how to optimize swimming pool layouts. A rectangular pool—simple yet versatile—sets the stage for thoughtful deck design, often the next step in creating a cohesive outdoor experience. When combined with the realistic total area of 400 square meters, including the deck, users seek precise measurements to balance form, function, and investment.
Breaking Down the Geometry: How Deep Is the Deck?
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Key Insights
We begin with the pool dimensions: 25 meters in length and 10 meters in width. Adding a consistent deck width $ x $ around the pool means extending each side by $ 2x $, resulting in new outer dimensions:
- Length: $ 25 + 2x $ meters
- Width: $ 10 + 2x $ meters
The total area including the deck is then:
$$ (25 + 2x)(10 + 2x) = 400 $$
Expanding this:
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$$
250 + 50x + 20x + 4x^2 = 400
\Rightarrow 4x^2 + 70x + 250 = 400
\Rightarrow 4x^2 + 70x - 150 = 0
$$
Dividing through by 2 to simplify:
$$ 2x^2 + 35x - 75 = 0 $$
Applying the quadratic formula $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $, we find:
$$ x =
