Question

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

Answer 1

Answer:

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,  

$P=2L+2W$

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

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

$\therefore 1600=2L+2W$   ….1

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

$L\times \ \:20=\ \:20\:L$

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

$2\:W \times \ \:5=\ \:10\:W$

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,

$\ \:13000 = \ \:20\:L + \ \:10\:W$  ….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,  

$\therefore L+W=800$

Subtracting L from both sides,  

$\therefore W=800-L$  ….3

Substituting equation 3 into equation 1 and simplifying,  

$13000=20L+10\left ( 800-L \right )$  

$13000=20L+\left ( 8000-10L \right )$  

$13000=10L+8000$  

$13000-8000=10L$  

$5000=10L$  

$500=L$  

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

$2L+2W=1600$  

$2\left ( 500 \right )+2W=1600$  

$1000+2W=1600$  

$2W=1600-1000$  

$2W=600$  

$W=300$  

So value of width is 300 feet.