A rectangular school banner has a length of 44 inches, a perimeter of 156 inches, and an area of 1496 square inches. The cheerleader make signs similar to the banner. The length of a sign is 11 inches. What is the perimeter and its area?

1 Answer
Jim G.
Jun 24, 2017

#"perimeter "=39" inches", "area "=93.5" sq inches"#

Explanation:

#"in similar figures the ratios of corresponding sides are equal"#

#"for similar rectangles the corresponding sides are the lengths"#
#"and widths"#

#"ratio of lengths (k ) "=11/44=1/4#

#• "perimeter of banner "=2l+2w=156#

#"where "l="length and " w=" width"#

#rArrw=1/2(156-(2xx44))=34" inches"#

#rArr"width of model "=1/4xx34=8.5" inches"#

#• " perimeter of model "=(2xx11)+(2xx8.5)#

#color(white)(xxxxxxxxxxxxxxxx) =39" inches"#

#"there are 2 possible approaches to calculating the"#
#"area of the model"#

#• " area " =lw=11xx8.5=93.5" sq inches"#

#color(red)"OR"#

#"area "=1496xx(1/4)^2=93.5" sq inches"#

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