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Problem solving your family has a rectangular pool that measures 18 feet by 9 feet. your family wants to put a deck around the pool but is not sure how wide to make the deck. determine how wide the deck should be when the total area of the pool and deck is 400 square feet. what is the width of the deck?

Respuesta :

jorel1380
Let w be the width of the deck. Then, using the total area, we get:
(9+2w)(18+2w)=400
4w²+54w-238=0
2w²+27w-119=0
(2w-7)(w+17)=0
w=-17 or 7/2
Using the positive value, we get a width of 3&1/2 ft. for the deck
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The width of the deck is [tex]3.5[/tex]feet.

Area of rectangle [tex]= length\times width[/tex]

Let [tex]x[/tex] be the width of the deck,

[tex]total\; length= 9+2x[/tex]

[tex]Total \; width = 18+2x[/tex]

Total area[tex]=400[/tex] (given)

[tex]400 = (9+2x)(18+2x)[/tex]

[tex]400=162+18x+36x+4x^2\\[/tex]

[tex]2x^2+27x+119=0[/tex]

Solve quadratic equation, we get

[tex](x-17)(x-3.5)=0[/tex]

[tex]x=-17 \; or\; 3.5[/tex]

So the width of the deck can not be negative.

Hence width of the deck is [tex]3.5[/tex] feet.

Learn more about rectangle here;

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