SOLUTION: A farmer normally plows a rectangular field 80ft by 120 ft. This year the farmer wants to expand the area of the field by 20%, by extending the width and length of the plowed area

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Question 67792: A farmer normally plows a rectangular field 80ft by 120 ft. This year the farmer wants to expand the area of the field by 20%, by extending the width and length of the plowed area an equal amount. How much wider and longer should the farmer plow the field to obtain a 20% increase in area?
Found 2 solutions by ankor@dixie-net.com, checkley71:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A farmer normally plows a rectangular field 80 ft by 120 ft. This year the farmer wants to expand the area of the field by 20%, by extending the width and length of the plowed area an equal amount. How much wider and longer should the farmer plow the field to obtain a 20% increase in area?
:
Determine the area of the original field: 80 * 120 = 9600 sq ft
:
Find the area of the larger field: 1.2 * 9600 = 11520 sq ft
:
Let x = number of feet added to the existing dimensions
:
(80+x)(120+x) = 11520
:
FOIL
9600 + 200x + x^2 = 11520
:
Arrange as a quadratic equation:
x^2 + 200x + 9600 - 11520
:
x^2 + 200x - 1920 = 0
:
Use the quadratic equation: a = 1; b = 200; c = -1920
:
x+=+%28-200+%2B-+sqrt%28+200%5E2+-+4+%2A+1+%2A+-1920+%29%29%2F%282%2A1%29+
:
x+=+%28-200+%2B-+sqrt%28+40000+-+%28-7680%29+%29%29%2F%282%29+
:
x+=+%28-200+%2B-+sqrt%28+47680+%29%29%2F%282%29+
:
x+=+%28-200+%2B+218.3575%29%2F%282%29+ it's the positive solution we want here
:
x+=+%2818.3575%29%2F%282%29+
:
x = 9.17875 ft
:
The new field: 89.17875 * 129.17875 = 11519.999 ~ 11520 sq ft



Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
CURRENT AREA=80*120=9600
TO INCREASE THIS AREA BY 20% IT MUST BE 9600*1.2=11520
THUS (80+X)(120+X)=11520
9600+120X+80X+X^2=11520
X^2+200X+9600-11520=0
X^2+200X-1920=0
USING THE QUADRATIC EQUATION WE GET
X=(-B+-SQRT[B^2-4AC])/2A
X=(-200+-SQRT[200*200-4*1*-1920])/2*1
X=(-200+-SQRT[40000+7680])/2
X=(-200+-SQRT47680])/2
X=(-200+-218.3578)/2
X=-200+218.3578)/2
X=18.3578/2
X=9.17875 ANSWER.