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 ) =1144=14

∙perimeter of banner =2l+2w=156

where l=length and w= width

⇒w=12(156−(2×44))=34 inches

⇒width of model =14×34=8.5 inches

∙ perimeter of model =(2×11)+(2×8.5)

××××××××=39 inches

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

∙ area =lw=11×8.5=93.5 sq inches

OR

area =1496×(14)2=93.5 sq inches

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