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The area of a rectangle is 80 sq ft. If the width is increased by 1 foot and the length is decreased by 1 foot, the new rectangle has area 90 sq ft. What is the perimeter of the original rectangle, in feet?

Jun 1, 2020

#1
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$$S_1*S_2 = 80$$

$$[S_1+1]*[S_2-1] = 90$$

$$S_1 = {80\over S_2}$$

$$[{80\over S_2}+1]*[S_2-1]=90$$

$$[{80+S_2\over S_2}]*[{S_2-1\over 1}]=90$$

$${{80S_2-80+(S_2)^2-S_2}\over S_2}=90$$

$${{80S_2-80+(S_2)^2-S_2}} =90S_2$$

$${{80S_2-80+(S_2)^2-S_2-90S_2}} =0$$

$${-80+(S_2)^2-11S_2} =0$$

$$(S_2)^2 -11S_2-80 =0$$

$$S_2=16$$

$$S_1 = 5$$

$$p = 42$$

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Jun 1, 2020