SOLUTION: Instead of walking along two sides of rectangular field, Frank took a shortcut along the diagonal, thus saving distance equal to half the length of the longer side. Find the length

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Question 661911: Instead of walking along two sides of rectangular field, Frank took a shortcut along the diagonal, thus saving distance equal to half the length of the longer side. Find the length of the long side of the field, given that the length of the short side is 156 meters.
I've been struggling with this question can you please help me . it will be very appreciated
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the length of the longer side. We know that the shorter side is 156 meters. We can use the Pythagorean Theorem to calculate the length of the diagonal:
d+=+sqrt%28x%5E2+%2B+156%5E2%29
If Frank had walked along two sides of the field, he would have walked x+156 meters. By walking along the diagonal, he saved half the length of the longer side, or x%2F2 meters.
So we have
sqrt%28x%5E2+%2B+156%5E2%29+=+x+%2B+156+-+x%2F2
sqrt%28x%5E2+%2B+156%5E2%29+=+x%2F2+%2B+156
Squaring both sides:
x%5E2+%2B+24336+=+x%5E2%2F4+%2B+156x+%2B+24336
x%5E2+=+x%5E2%2F4+%2B+156x
3%2Ax%5E2%2F4+=+156x
3%2Ax%2F4+=+156
%284%2F3%29%2A%283%2Ax%2F4%29+=+%284%2F3%29%2A156
x+=+208
The long side of the field is 208 meters.