SOLUTION: Last year Grandpa Jones had a small square garden. This year he has a square garden that is 112 sq feet in area. Each side of the new garden is 2 feet longer than triple each side

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Question 982004: Last year Grandpa Jones had a small square garden. This year he has a square garden that is 112 sq feet in area. Each side of the new garden is 2 feet longer than triple each side of the old garden. find the dimensions of each garden?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ ft = the side of the 1st garden
+3s+%2B+2+ ft = the side of the 2nd garden
given:
+%28+3s+%2B+2+%29%5E2+=+112+
+9s%5E2+%2B+12s+%2B+4+=+112+
+9s%5E2+%2B+12s+-+108+=+0+
Divide through by +3+
+3s%5E2+%2B+4s+-+36+=+0+
Use the quadratic formula:
+s+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+3+
+b+=+4+
+c+=+-36+
+s+=+%28+-4+%2B-+sqrt%28+4%5E2-4%2A3%2A%28-36%29+%29%29%2F%282%2A3%29+
+s+=+%28+-4+%2B-+sqrt%28+16+%2B+432+%29%29%2F6+
+s+=+%28+-4+%2B-+sqrt%28+448+%29%29+%2F+6+
+s+=+%28+-4+%2B+21.166+%29+%2F+6+
+s+=+17.166%2F6+
+s+=+2.861+
and
+3s+%2B+2+=+8.583+%2B+2+
+3s+%2B+2+=+10.583+
The side of the 1st garden is 2.861 ft
The side of the 2nd garden is 10.583 ft
------------------------------------
check:
+3s%5E2+%2B+4s+-+36+=+0+
+3%2A2.861%5E2+%2B+4%2A2.861+-+36+=+0+
+3%2A8.1853+%2B+11.444+-+36+=+0+
+24.5559+-+24.556+=0+
close enough
Hope I got it!