SOLUTION: Pat has a garden next to her house with the dimensions 3m by 10m. She wants to double the area of her garden by digging a border of even width around three of its sides. How wi

Question 118837:
Pat has a garden next to her house with the dimensions 3m by 10m. She wants to double the area of her garden by digging a border of even width around three of its sides. How wide of a border should she dig
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
3*10=30 METERS^2 IS PAT'S GARDEN AREA.
DOUBLING THIS AREA 2*30=60 METERS^2 IS THE TOYAL AREA.
NOW IT DEPENDS WHAT 3 SIDES SHE DIGS AROUND.
IF IT IS THE 3,10,3 SIDES THEN:
(3+X)(10+2X)=60
30+16X+2X^2=60
2X^2+16X+30-60=0
2X^2+16X-30=0
2(X^2+8X-15)=0
USING THE QUADRATIC EQUATION WE GET:
X=(-8+-SQRT[8^2-4*1*-15])/2*1
X=(-8+-SQRT[64+60])/2
X=(-8+-SQRT124)/2
X=(-8+-11.136)/2
X=(-8+11.136)/2
X=3.136/2
X=1.568 ANSWER FOR THE WIDTH OF THE BORDER.
----------------------------------------------------------------------
HOWEVER --- IF THE 3 SIDES ARE 10,3,10 THEN:
(10+X)(3+2X)=60
30+3X+20X+2X^2=60
2X^2+23X+30-60=0
2X^2+23X-30=0
X=(-23+-SQRT[23^2-4*2*-30])/2*2
X=(-23+-SQRT[529+240])/4
X=(-23+-SQRT769)/4
X=(-23+-27.73)/4
X=(-23+27.73)/4
X=4.73/4
X=1.18 ANSWER FOR THIS BORDER.
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