math

A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches. What is the ratio of the area of the school banner to the area of the sign?

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asked by g
  1. The areas of similar shapes are proportional to the square of their corresponding sides

    area of banner : area of sign = 54^2 : 17^2
    = 2916 : 289
    = appr 10.1 : 1

    OR, the long way ....

    area of banner = 54x36 = 1944 inches^2

    for the sign, we need the width
    17/54 = w/36
    w = 36(17/54) = 612/54 = 34/3

    area of sign = 17(34/3) = 578/3

    ratio of areas
    = 1944 : 578/3
    = 5832 : 578
    = 2916 : 289 , same as above

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    posted by Reiny

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