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if area is 47.5cm squared and length is 3cm longer than width, what is length and what is width?

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If a rectangle is 3cm longer than it's width and it's area is 47.5cm squared what is it's length and it's width, and how do you find them?

asked Mar 4, 2014 in GEOMETRY by dkinz Apprentice

1 Answer

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Let rectangle width(b) = xcm

Then length(l) wouldbe x+3cm.

A = l*b

47.5 = x(x+3)

47.5 = x^2+3x

Subtract 47.5 from each side.

x^2+3x-47.5 = 0

Compre it to quadratic equation ax^2+bx+c = 0

a = 1,b = 3, c = -47.5

x = [-b±√(b^2-4ac)]/2a

x = [-3±√(9+190)]/2

x = [-3±√199]/2

x = [-3±14.10]/2

x = (-3+14.10)/2 and x = (-3-14.10)/2

x = 11.10/2 and x = -17.10/2

x = 5.55 and x = -8.55

Rectangle has positive dimension.

So x = b = 5.55cm

3+x = l = 8.55cm

 

 

answered Mar 4, 2014 by ashokavf Scholar

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