So the area of the deck is
Area=(40+2w)w +45(2w)
solve for w.
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?
4 answers
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
= (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
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)
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)
Xxzx