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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

User Lou
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Answer:

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

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* \$\: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 * \$\: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.

User NichtJens
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