SOLUTION: The perimeter of a rectangular field is 44m and its area is 105m^2. Find the dimension of the field.

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Question 1137206: The perimeter of a rectangular field is 44m and its area is 105m^2. Find the dimension of the field.
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let P+ = perimeter
Let +A+ = area
Let +a+ = length
Let +b+ = width
----------------------------
+P+=+2a+%2B+2b+ m
+2a+%2B+2b+=+44+
(1) +a+%2B+b+=+22+
and
+A+=+a%2Ab+ m2
(2) +a%2Ab+=+105+
----------------------------
(1) +b+=+22+-+a+
(2) +a%2A%28+22+-+a+%29+=+105+
(2) +a%5E2+-+22a+=+-105+
(2) +a%5E2+-+22a+%2B+%2822%2F2%29%5E2+=+-105+%2B+%2822%2F2%29%5E2+
(2) +a%5E2+-+22a+%2B+121+=+-105+%2B+121+
(2) +%28+a+-+11+%29%5E2+=+16+
(2) +a+-+11+=+-4+ ( +square root of 16 gives the wrong answer )
(2) +a+=+7+
and
(1) +b+=+22+-+7+
(1) +b+=+15+
--------------------------
The dimensions are 7m by 15m
check:
+105+=+a%2Ab+
+105+=+7%2A15+
+105+=+105+
OK

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The semiperimeter (length plus width) is 44/2 = 22; the area (length times width) is 105.

Mentally, find two numbers whose product is 105 and whose sum is 22:
105*1 no...
35*3 no...
21*5 no...
15*7 AHA!

ANSWER: The field is 15m by 7m