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.