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