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
Jun 24, 2017
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"#
