SOLUTION: 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 th

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

RELATED QUESTIONS
Hector built a rectangular fish pond surrounded by a brick wall 3 m wide with an area of... (answered by josgarithmetic)

A rectangular pond's length is twice its width. The pond is surrounded on all sides by a... (answered by mananth)

A rectangular fish pond is 8ft longer than it is wide. A wooden walk 2 ft wide is placed... (answered by addingup)

The perimeter of a figure is the sum of the lengths of its sides. A circular fish pond... (answered by rothauserc)

A circular brick path is being installed around a circular pond. The pond has a... (answered by Fombitz)

A pond is enclosed by a wooden deck that is 3 feet wide. The fence surrounding the deck... (answered by Alan3354)

A pond is enclosed by a wooden deck that is 3 feet wide.The fence surrounding the deck is (answered by mananth,ikleyn)

A pond is enclosed by a wooden deck that is 3 feet wide.The fence surrounding the deck... (answered by ikleyn)

a circular pond has a radius of 10 feet. there are plans to build a paved path around the (answered by jim_thompson5910)