#1**+3 **

The scale drawing of a rectangular yard measures (2x^{2} + 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 ) = (2x^{2} + 2)(x + 4)

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

Substitute (2x^{2} + 2)(x + 4) for area of scale drawing

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

Cross multiply

(140)(2x^{2} + 2)(x + 4) = 12(area of actual yard)

Divide both sides of the equation by 12

(140)(2x^{2} + 2)(x + 4) / 12 = area of actual yard

area of actual yard = (140)(2x^{2} + 2)(x + 4) / 12

Expand the right side of the equation

area of actual yard = (140)(2x^{3} + 8x^{2} + 2x + 8) / 12

area of actual yard = (280x^{3} + 1120x^{2} + 280x + 1120) / 12

Divide the numerator and denominator by 4

area of actual yard = (70x^{3} + 280x^{2} + 70x + 280) / 3

hectictar May 19, 2019