A swimming pool 20 m long and 10 m wide is surrounded by a deck of uniform width. The total area of the swimming pool and the deck is 704 m². Find the width of the deck.

S = 704 m 2 w i d t h o f t h e d ec k − x S = a ⋅ b ( 10 + 2 x ) ( 20 + 2 x ) = 704 200 + 20 x + 40 x + 4 x 2 − 704 = 0 4 x 2 + 60 x − 504 = 0 / : 4
x 2 + 15 x − 126 = 0 a = 1 , b = 15 , c = − 126 Δ = b 2 − 4 a c = 1 5 2 − 4 ⋅ 1 ⋅ ( − 126 ) = 225 + 504 = 729 x 1 ​ = 2 a − b − Δ ​ ​ = 2 − 15 − 729 ​ ​ = 2 − 15 − 27 ​ = 2 − 42 ​ = − 21 c an n o t b e n e g a t i v e x 2 ​ = 2 a − b + Δ ​ ​ = 2 − 15 + 729 ​ ​ = 2 − 15 + 27 ​ = 6 m A n s w er : w ai s t w i d t h i s 6 m

Answered by Lilith | 2024-06-10

Let x = width of the deck. Therefore total area of pool : (10+2x)m*(20+2x)m = 704 m^2 ( 200 + 20x + 40x + 4x^2 ) m^2 = 704 m^2 (200 + 60x + 4x^2) = 704 4x^2 + 60x = 704-200 4x^2 + 60x = 504 4x^2 + 60x - 504 = 0 4(x^2 + 15x - 126) = 0 (x+21) * (x-6) = 0 Therefore x, the deck's width is 6m (it can't be -21 as width is measured as a positive value) Kindly press the Thank You button and indicate this as best answer if it answers your question correctly. Thanks.

Answered by leonghw | 2024-06-10

The width of the deck surrounding the swimming pool is 6 meters. This was determined by creating an equation for the total area, solving a quadratic equation, and finding a valid positive solution. The resulting width of the deck avoids negative values, confirming its correctness.
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Answered by Lilith | 2024-11-04