Arectangular garden has a width of 5 feet and a length of 10 feet. If an equal amount is added to both the width and the length, the area is increased to 104 square feet. What is this amount?

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Answer 1 · 2018-06-21T13:34:38

#color(blue)(3 " feet")#

We first notice that the length is twice the width. If we let the:

#"Width" = x# and the #"Length"=2x#

We need to add an equal amount to both of these. Let this amount be #m#

So we have for new area:

#(x+m)(2x+m)=104#

Substituting our known value for #x#

#(5+m)(10+m)=104#

#m^2+15m+50=104#

#m^2+15m-54=0#

Factor:

#(m+18)(m-3)=0=>m=3 and m=-18#

We can't have negative length, so only #m=3#.

Therefore we need to add #3 " feet"# to both the length and width.