Originally a rectangle was twice as long as it is wide. When 4m were added to its length and 3m subtracted from its width, the resulting rectangle had an area of 600m^2. How do you find the dimensions of the new rectangle?

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Answer 1 · 2016-04-26T09:30:57

Original width #=18 # metres
Original length #=36# mtres

The trick with this type of question is to do a quick sketch. That way you can see what is happening and devise a method of solution.

Tony B

Known: area is #"width "xx" length"#

#=>600 =(w-3)(2w+4)#

#=>600=2w^2+4w-6w-12#

Subtract 600 from both sides

#=>2w^2-2w-612=0#

#=>(2w-36)(w+17)=0#

#=> w=-17#

It is not logical for a length to be negative in this context
so #w!=-17#

#w= 18#

#=> L = 2xx18=36#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check

#(36+4)(18-3) = 40xx15 =600 m^2#