Question

A rectangular wimming pool is 40 ft wide and 45 ft long. It is surrounded on all four sides by a wooden deck of fixed width. The total area enclosed within the perimeter of the deck is 2354 sq ft. What is the width of the deck?

Answer 1

So the area of the deck is

Area=(40+2w)w +45(2w)

solve for w.

Answer 2

area of pool and deck
= (40+2x)(45+2x)
= 2354

1800 + 170x + 4x^2 = 2354
2x^2 + 85x - 277 = 0
by formula
x = 3.04 or a negative

the deck is 3.04 ft wide

check: length = 45+2(3.04) = 51.08
width = 40 + 2(3.04) = 46.08
area = 51.08 x 46.08 = appr 2353.8

Answer 3

hmmm. unfortunately, we only have the total area of pool+deck is 2354.

deck area = total area - pool area
deck area = 2354 - 40*45 = 554

now you can solve bob's equation for the deck width, with the small correction that there are two short sides:

Area=(40+2w)(2w) +45(2w)

Answer 4

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