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 May 19, 2019
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The scale drawing of a rectangular yard measures (2x2 + 2) by (x + 4). If the area of the scale drawing and the

area of the actual yard are in the ratio 12:140, find an expression for the area of the actual yard in expanded form.

 

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area of scale drawing  =  ( length )( width )  =  (2x2 + 2)(x + 4)

 

area of scale drawing / area of actual yard  =  12 / 140

                                                                                        Substitute  (2x2 + 2)(x + 4)  for  area of scale drawing

(2x2 + 2)(x + 4) / area of actual yard  =  12 / 140            Now we just have to solve for  area of actual yard

                                                                                        Cross multiply

(140)(2x2 + 2)(x + 4)  =  12(area of actual yard)

                                                                                        Divide both sides of the equation by  12

(140)(2x2 + 2)(x + 4) / 12  =  area of actual yard

 

area of actual yard  =  (140)(2x2 + 2)(x + 4) / 12

                                                                                        Expand the right side of the equation

area of actual yard  =  (140)(2x3 + 8x2 + 2x + 8) / 12

 

area of actual yard  =  (280x3 + 1120x2 + 280x + 1120) / 12

                                                                                                 Divide the numerator and denominator by  4

area of actual yard  =  (70x3 + 280x2 + 70x + 280) / 3

 May 19, 2019

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