Word Problem

Question

The perimeter of a rectangular field is 300 meters. This field is to be fenced along three sides only. The fencing along its two lengths and one width is to be done at $50 per meter. If the total cost of fencing is $12,000, what are the field's dimensions?

Answer 1

P=2l+2w

300=2l+2w

$12,000/$50=240 meters along three sides only

240=2l+w

300=2l+2w

subtract the first equation from the second equation

60=w

w=60 m

240=2l+60

240-60=2l

180=2l

l=90 m

dimensions are 90 m by 60 m by 90 m

Answer 2

HI,

 

As mentioned perimeter of the rectangle is 300m. 

That is Perimeter of a rectangle = 2l+2b = 300

 

2(l+b) = 300

L+b = 150

Hence L = 150 - b or b= 150- l

 

Now also mentioned that fencing is needed only for two lengths and one width and for each meter it costs $50.

 

Therefore 

 

{2l + b}*50= 12000

 

And we know that L= 150-b or b=150-l

 

Hence we get

 

{2l + (150-l)}*50 = 12000

 

Solving the above expression we get 

 

100l + 7500 - 50l = 12000

 

50l = 4500

 

Therefore  l =90m

 

Substituting this in b = 150-l

 

B= 150-90 = 60m