SOLUTION: A factory measuring 60 m by 80 m is surround by a lawn of uniform width. If the area is 57 m2 less than the factory find the width of the lawn.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A factory measuring 60 m by 80 m is surround by a lawn of uniform width. If the area is 57 m2 less than the factory find the width of the lawn.       Log On


   

Question 1083209: A factory measuring 60 m by 80 m is surround by a lawn of uniform width. If the area is 57 m2 less than the factory find the width of the lawn.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the factory is
+60%2A80+=+4800+ m2
The area of the lawn is
+4800+-+57+=+4743+
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The combined area of factory and lawn is
+4800+%2B+4743+=+9543+
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Let +x+ = the width of the lawn
I can now say:
+%28+60+%2B+x+%29%2A%28+80+%2B+x+%29+=+9543+
+4800+%2B+140x+%2B+x%5E2+=+9543+
+x%5E2+%2B+140x+-+4743+=+0+
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+140+
+c+=+-4743+
-----------------
+x+=+%28-140+%2B-+sqrt%28+140%5E2-4%2A1%2A%28-4743%29+%29%29+%2F+%282%2A1%29+
+x+=+%28-140+%2B-+sqrt%28+19600+%2B+18972++%29%29+%2F+2+
+x+=+%28-140+%2B-+sqrt%28+38572++%29%29+%2F+2+
+x+=+%28+-140+%2B+196.398+%29+%2F+2+
+x+=+56.398%2F2+
+x+=+28.199+
The width of the lawn is about 28.2 m
-------------------------------------
check:
+%28+60+%2B+x+%29%2A%28+80+%2B+x+%29+=+9543+
+%28+60+%2B+28.2+%29%2A%28+80+%2B+28.2+%29+=+9543+
+88.2%2A108.2+=+9543+
+9543.24+=+9543+
Error due to rounding off, I think
check the math

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

A factory measuring 60 m by 80 m is surround by a lawn of uniform width. If the area is 57 m2 less than the factory find the width of the lawn. 
Width of the lawn: highlight_green%28matrix%281%2C2%2C+14.099389%2C+m%29%29