SOLUTION: A rectangular field is enclosed by a fence on three sides and a wall on the fourth side. The total length of the fence is 320 yards. If the field has a total perimeter of 400 yard

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Question 1132749: A rectangular field is enclosed by a fence on three sides and a wall on the fourth side. The total length of the
fence is 320 yards. If the field has a total perimeter of 400 yards, what are the dimensions of the field?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
.
If x and y are the dimensions under the question, then from the condition you have these two equations


    2x +  y = 320     yards   (1)
    2x + 2y = 400     yards   (2)


Subtract eq(1) from eq(2). You will get  y = 400-320 = 80 for one dimension  (y).


Then for x you have from eq(1)  2x + 80 = 320  ====>  2x = 320-80 = 240  ====>  x = 240/2 = 120.



ANSWER.  The dimensions are 120 and 80 yards.  80 yards go along the wall.  120 yards go perpendicularly to the wall.


Solved.


Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The fence, making 3 sides of the field, has a total length of 320 yards; the perimeter of the whole rectangular field is 400 yards. So the length of the field along the wall is 400-320 = 80 yards.

So one dimension of the field is 80 yards. That makes 2 sides of length 80, for a total of 160 yards.

Since the perimeter of the whole field is 400 yards, the sum of the lengths of the other two sides is 400-160 = 240 yards. So the other dimension of the field is 240/2 = 120 yards.

ANSWER: 80 by 120 yards
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