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02-09-2018
Mathematics

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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 cheerleaders make signs similar to the banner. the length of a sign is 11 inches. what is its perimeter and its area?

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02-09-2018

The smaller sign has dimensions that are 11/44 = 1/4 those of the larger banner, so its perimeter is

... (1/4)×156 inches = 39 inches . . . perimeter

and its area is

... (1/4)²×(1496 in²) = 93.5 in² . . . . . . area

_____

The linear dimensions of similar figures all have the same scale factor. Those include length, width, perimeter, diameter, radius, height, or any other linear dimension.

The area dimensions of similar figures have a scale factor that is the square of the linear dimension scale factor. (Area is the product of two linear dimensions, each of which has the linear dimension scale factor.)

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