A rectangle has an area of #150# #cm^2#. It has a length that is #5# #cm# longer than its width. What is the rectangle's length?

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Answer 1 · 2017-07-03T00:46:20

length #=15cm#
width#=10cm#

#l*w=A#

let #w=x#

let #l=x+5#

#A=(x+5)*x#

and distribute: #150=x^2+5x#

move everything to one side: #x^2+5x-150=0#

factor: #(x+15)*(x-10)=0#

#x+15=0# ; #x=-15#
or
#x-10=0# ; #x=10#
#x!=-15# so #x=10#

length #=15cm#
width#=10cm#