SOLUTION: A director of a zoo wants to use 170 meters of fencing to enclose a petting area of 1750 meters squared. Find the dimensions of the petting area.

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Question 17885: A director of a zoo wants to use 170 meters of fencing to enclose a petting area of 1750 meters squared. Find the dimensions of the petting area.
Answer by whisper(27) About Me  (Show Source):
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The given information is:
170 meters of fencing so that the perimeter is 170.
The area is to be 1750.
The formula for area is lxw=a
The formula for perimeter is 2l+2w=p
2l+2w=170
Divde by through by 2
2l/2+2w/2=170/2
l+w=85
subtract w or the width from both sides to get length in terms of width.
l+w-w=85-w
l+0=85-w
l=85-w
So now again recall the formula lxw=a
(85-w)w=1750
85w-w^2=1750
Now get everything on one side of the equation by subtracting 1750 from both sides
-w^2+85w-1750=85-1750
-w^2+85w-1750=0
You could solve for w here by using the quadratic formula but to solve by factoring it will be easier to multiply through by -1
-1(-w^2)+-1(85w)+-1(-1750)=0(-1)
w^2-85w+1750=0
(w-50)(w-35)=0
w-50 = 0 or w-25=0
So w=50 or w=25
Please don't hesitate to ask if you have further questions!