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
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):
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.
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.
