Question

A fence is to be built to enclose a rectangular area of 450 square feet. The fence along three sides is to be made of a material that costs ​$3 per foot. The material for the fourth side costs ​$9 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.

Answer 1

Answer: 25 by 50 ft

Hope this helps

Answer 2

The dimensions of the rectangle will allow for the most economical fence to be built are 30 feet by 15 feet

Given that, rectangular area=450 square feet.

What is the formula to find the area of a rectangle?

The formula to find the area of a rectangle is Area=Length×Breadth.

Let the length of the rectangle be x and the breadth of the rectangle be y.

Now, 450=xy.

x=450/y

The cost of three sides is $3 per foot.

That is, 3x+3x+3y

The cost on the fourth side is $9 per foot.

That is, 9y

Total cost=6x+12y

Now, Total cost=6×450/y+18y

Let the minimum cost be 0.

2700/y+12y=0

⇒2700/y²-12=0

⇒12y²=2700

⇒y=15 feet

So, 450/15=x=30 feet.

Therefore, the dimensions of the rectangle are 30 feet by 15 feet.

To learn more about the area of a rectangle visit:

https://brainly.com/question/20693059.

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