Question 126637
The length of a rectangle is 1cm greater than twice the width. If each dimension were increased by 5cm, the area would be at least 150cm^2 greater. Find the least possible dimensions.
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Let the width be "x" cm ; length is "2x+1" cm
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Changing dimensions:
width is "x+5" cm ; length is "2x+6" cm
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EQUATION:
(x+5)(2x+6) >= 150
Divide both sides by 2 to get:
(x+5)(x+3) >= 75
x^2+8x-60 >= 0
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x <= [-8 +- sqrt(64-4*-60)]/2

x <= [-8 +- sqrt(304)]/2

x = [-8 +- 17.435596]/2

0 <= x <= 4.717798 
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width is "x+5" cm ; length is "2x+6" cm
0 <  width <=9.717798
15.435596 <= length  < 150 

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Cheers,
stan H.