How to find the length and the width of this rectangle? Thanks!

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1 Answer
Apr 20, 2018

#x+3" and "2x+7#

Explanation:

#"since area "="length "xx"width"#

#"then the product of the factors of "2x^2+13x+21#
#"are the length and width"#

#"factoring using the a-c method"#

#"the factors of the product "2xx21=42#

#"which sum to + 13 are + 6 and + 7"#

#"split the middle term using these factors"#

#2x^2+6x+7x+21larrcolor(blue)"factor by grouping"#

#=color(red)(2x)(x+3)color(red)(+7)(x+3)#

#"take out the "color(blue)"common factor "(x+3)#

#=(x+3)(color(red)(2x+7))#

#"the length and width are "x+3" and "2x+7#