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?

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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?

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Answer 1 · 2017-06-24T14:31:49

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

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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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

Explanation:

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