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If each dimension of a rectangle decreases by 1, its area will decrease from 2017 to 1917. What will be the area of the rectangle if each of its dimensions increases by 1?

 Jun 28, 2021
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If each dimension of a rectangle decreases by 1,
its area will decrease from 2017 to 1917.
What will be the area of the rectangle
if each of its dimensions increases by 1?

 

\(\text{Let $ab=2017$ }\)

 

\(\begin{array}{|lrcll|} \hline \text{decreases by $1$ :} & 1917 &=& (a-1)(b-1) \\ & 1917 &=& ab-(a+b) +1 \qquad (1) \\\\ \text{increases by $1$ :} & x &=& (a+1)(b+1) \\ & x &=& ab+(a+b) +1 \qquad (2) \\\\ \hline (1)+(2):& 1917+x &=& ab-(a+b) +1 + ab+(a+b) +1 \\ & 1917+x &=& 2ab+ 2 \\ & x &=& 2ab+ 2 -1917 \\ & x &=& 2ab -1915 \quad | \quad \mathbf{ab=2017} \\ & x &=& 2*2017 -1915 \\ & x &=& 2119 \\ \hline \end{array}\)

 

The area of the rectangle
if each of its dimensions increases by 1 is 2119

 

laugh

 Jun 28, 2021

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