The area of a rectangular plot 24 feet long and 16 feet wide will be doubled by adding an equal distance to each side of the plot. What is the distance added to each side?

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Answer 1 · 2018-04-27T12:57:29

#color(blue)(8 \ \ \"feet")#

Area of current plot:

#24xx16=384#

We need to double this:

Area of new plot:

#2xx384=768#

Let #x# be the amount added to each side:

#:.#

#(24+x)(16+x)=768#

Expanding brackets:

#x^2+40x-384=0#

Factor:

#(x+48)(x-8)=0=>x=-48 and x=8#

We can't have negative area, so only #x=8#.