SOLUTION: jackie mows a uniform width around her 30m by 20m rectangular lawn and leaves a patch of lawn that is 60% of the original area what is the width of the strip

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Question 697179: jackie mows a uniform width around her 30m by 20m rectangular lawn and leaves a patch of lawn that is 60% of the original area what is the width of the strip
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The original area is +30%2A20+=+600+ m^2
The area of patch left is +.6%2A600+=+360+
Let +x+ = the uniform width of mowed part
The unmowed patch is +30+-+2x+ by +20+-+2x+
+%28+30+-+2x+%29%2A%28+20+-+2x+%29+=+360+
+600+-+40x+-+60x+%2B+4x%5E2+=+360+
+4x%5E2+-+100x+%2B+240+=+0+
+x%5E2+-+25x+%2B+60+=+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-25+
+c+=+60+
+x+=+%28-%28-25%29+%2B-+sqrt%28+%28-25%29%5E2+-+4%2A1%2A60+%29%29+%2F+%282%2A1%29+
+x+=+%28+25+%2B-+sqrt%28+625+-+240+%29%29+%2F+2+
+x+=+%28+25+%2B-+sqrt%28+385+%29%29+%2F+2+
+x+=+%28+25+%2B-+19.6214%29+%2F+2+
+x+=+5.3786+%2F+2+
+x+=+2.6893+
The width of the strip is 2.6893 m
check answer:
+%28+30+-+2x+%29%2A%28+20+-+2x+%29+=+360+
+%28+30+-+5.3786+%29%2A%28+20+-+5.3786+%29+=+360+
+24.6214+%2A+14.6214+=+360+
+359.9993+=+360+
close enough