SOLUTION: A 10-ft by 20-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 136ft squared, how wide is the walkway?

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Question 563364: A 10-ft by 20-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 136ft squared, how wide is the walkway?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If x = the width of the walkway, the
length and width both increase by +2x+
given:
+%28+10+%2B+2x+%29%2A%28+20+%2B+2x+%29+=+10%2A20+%2B+136+
+4%2A%28+5+%2B+x+%29%2A%28+10+%2B+x+%29+=+200+%2B+136+
+4%2A%28+50++%2B+10x+%2B+5x+%2B+x%5E2+%29+=+336+
+x%5E2+%2B+15x+%2B+50+=+84+
+x%5E2+%2B+15x+-+34+=+0+
Use quadratic equation
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+15+
+c+=+-34+
+x+=+%28-15+%2B-+sqrt%28+15%5E2+-+4%2A1%2A%28-34%29+%29%29%2F%282%2A1%29+
+x+=+%28-15+%2B-+sqrt%28+225+%2B+136+%29%29+%2F+2+
+x+=+%28-15+%2B-+sqrt%28+361+%29%29+%2F+2+
+x+=+%28-15+%2B+19%29+%2F+2+
+x+=+4%2F2+
+x+=+2+ ( I can ignore the (-) square root )
The walkway is 2 ft wide
check:
+%28+10+%2B+2%2A2+%29%2A%28+20+%2B+2%2A2+%29+=+10%2A20+%2B+136+
+14%2A24+=+336+
+336+=+336+
OK