SOLUTION: a 20ft by 40ft rectangular swimming pool is surrounded by a walkway of uniform width. if the total area of the walkway is 544ft^2, how wide is the walkway?

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Question 494635: a 20ft by 40ft rectangular swimming pool is surrounded by a walkway of uniform width. if the total area of the walkway is 544ft^2, how wide is the walkway?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the pool plus the area of the walkway is
+544+%2B+20%2A40+=+544+%2B+800+
+544+%2B+800+=+1344+ ft2
The dimensions of the pool plus walkway are:
+%2820+%2B+2x%29%2A%2840+%2B+2x%29+
+%2820+%2B+2x%29%2A%2840+%2B+2x%29+=+1344+
+800+%2B+80x+%2B+40x+%2B+4x%5E2+=+1344+
+4x%5E2+%2B+120x+-+544+=+0+
+x%5E2+%2B+30x+-+136+=+0+
Use the quadratic equation
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+30+
+c+=+-136+
x+=+%28-30+%2B-+sqrt%28+30%5E2+-+4%2A1%2A%28-136%29+%29%29%2F%282%2A1%29+
x+=+%28-30+%2B-+sqrt%28+900+%2B+544+%29%29+%2F+2+
x+=+%28-30+%2B-+sqrt%28+1444+%29%29+%2F+2+
+x+=+%28-30+%2B+38%29+%2F+2+
+x+=+4+
+20+%2B+2x+=+28+
+40+%2B+2x+=+48+
The walkway is 4 ft wide
check:
+%2820+%2B+2x%29%2A%2840+%2B+2x%29+=+1344+
+28%2A48+=+1344+
+1344+=+1344+
OK