Find the original dimension of the rectangle
By Emma Terry •
A rectangle is 4 times as long as it is wide. If the length is increased by 4 inches and the width is decreased by 1 inch, the area will be 60 square inches. What were the dimensions of the original rectangle? Explain your answer.
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$\begingroup$Hint:
Denote its original width by $x$ and find an expression in $x$ for the area of the reformed rectangle. It should equalize $60$ so...
$\endgroup$ 4 $\begingroup$$$\ Width=a, Length=4a , $$ $$\text {so the total original area is: }\ A=4a^2$$ $$\text {now we know that the new area is}$$ $$\ A'=(4a+4)(a-1)=4a^2-4a+4a-4=4a^2-4=60$$ $$\text{so }\ 4a^2=A=64$$ $$\ a^2=64/4=16$$ $$\ a=4$$ $$\text{so}\ Width=4\text{ and }\ Length=16$$ $$\text{(all expressed in inches)}$$
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