SOLUTION: }llA parcel of land is 5 ft longer than it is wide. Each diagonal from one corner to the opposite corner is 145 ft long. What are the dimensions of the parcel?

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Question 1121931: }llA parcel of land is 5 ft longer than it is wide. Each diagonal from one corner to the opposite corner is 145 ft long. What are the dimensions of the parcel?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width = +x+
Length = +x+%2B+5+
————————————
+x%5E2+%2B+%28+x+%2B+5+%29%5E2+=+145%5E2+
+x%5E2+%2B+x%5E2+%2B+10x+%2B+25+=+21025+
+2x%5E2+%2B+10x+-+21000+=+0+
+x%5E2+%2B+5x+-+10500+=+0+
+%28+x+%2B+105+%29%2A%28+x+-+100+%29+=+0+ ( by looking at it )
+x+=+100+ ( needs to be positive )
+x+%2B+5+=+105+
The parcel is 100 x 105
—————————————-
Check:
+100%5E2+%2B+105%5E2+=+145%5E2+
+10000+%2B+11025+=+21025+
+21025+=+21025+
OK

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


Since the length of the diagonal is a whole number, and the difference between the side lengths is a whole number, the answer is going to have to be a Pythagorean triple.

We can make a "scale model" of the parcel of land by dividing everything by 5; that makes the length 1 more than the width, and the diagonal is 29.

Do you recognize a Pythagorean triple with hypotenuse 29? It is (20,21,29).

So the dimensions of the scale model rectangle are 20x21; the dimensions of the actual parcel are 100x105.