Question 876273: A rectangular pond is surrounded by a tile path that is y feet wide all the way around. The length of the fish pond with the border is 10 feet. The width of the fish pond with the border is 14 feet. The area of the fish pond is 24 square feet.
A. Write an algebraic expression for the length of the fish pond.
B. Write an algebraic expression for the width of the fish pond.
C. Write an algebraic equation for the area of the fish pond.
Thank you! :)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let l be length of fish pond, w be the width of fish pond, A = area of fish pond and y is width of the tile path all the way round, then
l + y = 10
w + y = 14
l * w = 24
A) w = 24/l
24/l + y = 14
y = 14 - 24/l
l + 14 - 24/l = 10
multiply both sides of = by l
l^2 + 14l - 24 = 10l
l^2 + 4l - 24 = 0
l = (-b + square root(b^2 -4ac))/2a = (-4 + square root(16 - 4*1*-24)) / 2*1 = 3.29
l = (-b + square root(b^2 -4ac))/2a = (-4 - square root(16 - 4*1*-24)) / 2*1 = -7.29
B) l = 24/w, then
24/w + y = 10
y = 10 - 24/w
w + (10 - 24/w) = 14
w + 10 - 24/w = 14
multiply both sides of = by w
w^2 + 10w -24 = 14w
w^2 - 4w -24 = 0
w = (-b + square root(b^2 -4ac))/2a = (4 + square root(16 - 4*1*-24)) / 2*1 = 7.29
w = (-b + square root(b^2 -4ac))/2a = (4 - square root(16 - 4*1*-24)) / 2*1 = -3.29
we chose the positive values for l and w
l = 3.29, w = 7.29
C) A = l * w = 24
A = 3.29 * 7.29 = 23.98 approx 24
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