charliesutton23
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# A rectangle whose perimeter is 80 m has an area of 384 m^2. Find the dimensions of the rectangle.

$2a+2b=80 \ /:2\ \ \ \Rightarrow\ \ \ \ a+b=40\ \ \ \Rightarrow\ \ \ a=40-b\\ \\a\cdot b=384\ \ \ \ \Rightarrow\ \ \ (40-b)\cdot b=384\ \ \ \ \Rightarrow\ \ \ -b^2+40b-384=0\\ \\ \Delta=40^2-4\cdot (-1)\cdot(-384)=1600-1536=64\ \ \ \Rightarrow\ \ \ \sqrt{\Delta} =8\\ \\b_1= \frac{-40-8}{2\cdot(-1)}= \frac{-48}{-2} =24\ \ \ \ \Rightarrow\ \ \ a_1=40-b_1=40-24=16 \\ \\b_2= \frac{-40+8}{2\cdot(-1)}= \frac{-32}{-2} =16\ \ \ \ \Rightarrow\ \ \ a_2=40-b_2=40-16=24$ $Ans.\ The\ dimensions\ of\ the\ rectangle:\ \ \ 16\ m\ \ \ and\ \ \ 24\ m$