Consider the following problem: A rectangular lot whose perimeter is 1600 feet is fenced along three sides. An expensive fencing along the lot's length costs $20 per foot. An inexpensive fencing along the two side widths costs only $5 per foot. The total cost of the fencing along the three sides comes to $13,000. What are the lot's dimensions

The dimensions of rectangular lot is Length=500 feet and Width=300 feet

Step-by-step explanation:

The formula for perimeter of rectangle is given by,  

Where, L = length, W = width and P = Perimeter.  

According to given data, rectangular lot has a perimeter of 1600 feet. Therefore,  

 ….1

Now, cost of fencing along one length is given as $ 20 per feet. So total cost of one length is,  

Similarly, cost of fencing along two width is given as $ 5 per feet. So total cost of two width is,  

Total cost of fencing along three sides is given as $13000. Therefore,  

Total cost = Cost of fencing of one length + Cost of fencing of two width

Substituting the value,

 ….2

So, there is two equations and two unknown. Solve it by substitution method.

Solving equation 1 for W.

Dividing both sides of equation by 2,  

Subtracting L from both sides,  

 ….3

Substituting equation 3 into equation 1 and simplifying,  

So value of length is 500 feet. Substituting the value of L in equation 1 and simplifying,  

So value of width is 300 feet.  

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.