Thread: Area Word Problems

1) A rectangular garden is bounded on one side by a river and is to be fenced in on the three other sides. Fencing material for the side parallel to the river is $30 per foot. Materials for the two other sides cost $10 per foot. What are the dimensions of the garden of largest possible area if $1200 is to be spent for fencing material?

2) A rectangular piece of cardboard measuring 20 inches by 32 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each square. What is the maximum volume of this box?

1) may be not enough info.

2) (20 - 2x)(32 - 2x)(x) cubic inches

Originally Posted by NRS11

1) A rectangular garden is bounded on one side by a river and is to be fenced in on the three other sides. Fencing material for the side parallel to the river is $30 per foot. Materials for the two other sides cost $10 per foot. What are the dimensions of the garden of largest possible area if $1200 is to be spent for fencing material?

2) A rectangular piece of cardboard measuring 20 inches by 32 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each square. What is the maximum volume of this box?

1) let the distance of the fence opposite to the river be x and that of the adjacent side be y. Then 30x+20y=1200, isolate x, and the area is x*y. You only have to complete the square after i think

Originally Posted by NRS11

1) A rectangular garden is bounded on one side by a river and is to be fenced in on the three other sides. Fencing material for the side parallel to the river is $30 per foot. Materials for the two other sides cost $10 per foot. What are the dimensions of the garden of largest possible area if $1200 is to be spent for fencing material?
...

Let r be the distance of the fence parallel to the river.
Let s be the length of the fence perpendicular to the river.
Max Money: $1200 = $30*r + 2*$10*s
Max Area: r*s




isolate r


substituting that in the area equation





take the derivitive and determine the value of s when the slope is zero.



solve that to get the value of s.
plug that back into the equation above to compute r.

How that helps

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