SOLUTION: A concrete path of a fixed width will be added around a rectangular garden that measures 10 feet by 13 feet. If there is enough material to cover 108 square feet, how wide will the

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Question 890813: A concrete path of a fixed width will be added around a rectangular garden that measures 10 feet by 13 feet. If there is enough material to cover 108 square feet, how wide will the concrete path be?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The rectangular garden + the concrete path
will measure +10+%2B+2x+ by +13+%2B+2x+
----------------
The area of the concrete path alone will be:
+%28+10+%2B+2x+%29%2A%28+13+%2B+2x+%29+-+10%2A13+
You are given that:
+%28+10+%2B+2x+%29%2A%28+13+%2B+2x+%29+-+10%2A13+=+108+
+130+%2B+26x+%2B+20x+%2B+4x%5E2+-+130+=+108+
+4x%5E2+%2B+46x+-+108+=+0+
+2x%5E2+%2B+23x+-+54+=+0+
Use the quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+2+
+b+=+23+
+c+=+-54+
+x+=+%28+-23+%2B-+sqrt%28+23%5E2+-+4%2A2%2A%28-54%29+%29%29+%2F+%282%2A2%29+
+x+=+%28+-23+%2B-+sqrt%28+529+%2B+432+%29%29+%2F+4+
+x+=+%28+-23+%2B-+sqrt%28+961+%29%29+%2F+4+
+x+=+%28+-23+%2B+31+%29+%2F+4+
+x+=+8%2F4+
+x+=+2+
--------------
The width of the concrete path is 2 ft
check:
+%28+10+%2B+2x+%29%2A%28+13+%2B+2x+%29+-+10%2A13+=+108+
+%28+10+%2B+2%2A2+%29%2A%28+13+%2B+2%2A2+%29+-+10%2A13+=+108+
+%28+10+%2B+4+%29%2A%28+13+%2B+4+%29+-+10%2A13+=+108+
+14%2A17+=+130+=+108+
+238+-+130+=+108+
+108+=+108+
OK