The area of a rectangle is #5 4/5# square meters. The width of the rectangle is #2 1/4# meter. How long is the rectangle?

1 Answer
mason m
Dec 17, 2015

#2 26/45# #"meters"#

Explanation:

First, convert the mixed numbers into improper fractions.

#"area"=5 4/5=5+4/5=25/5+4/5=29/5#

#"width"=2 1/4=2+1/4=8/4+1/4=9/4#

Next, we need to know that the area of a rectangle is equal to its length times its width, expressed algebraically as

#A=lw#

From the question, we know that

#29/5=lxx9/4#

To find just #l#, the length, multiply both sides by #4/9# (the reciprocal of #9/4#).

#29/5xx4/9=lxxcolor(red)(cancel(color(black)(9)))/color(blue)(cancel(color(black)(4)))xxcolor(blue)(cancel(color(black)(4)))/color(red)(cancel(color(black)(9#

#l=(29xx4)/(5xx9)=116/45=90/45+26/45=2 26/45#

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