Answer:
The length of the original rectangle is 8.
Step-by-step explanation:
If we call w the width and call L the length of the rectangle then the perimeter is calculated by the following equation:
[tex]2w+2L=P[/tex]
In this case we know that the perimeter P is: P=24
Then:
[tex]2w+2L=24[/tex]
If we call the new width of the rectangle w 'then
[tex]w '= 3w[/tex]
If we call the new length of the rectangle L 'then
[tex]L '= 0.5L[/tex]
Therefore:
[tex]2w'+2L'=24[/tex]
[tex]2(3w)+2(0.5L)=24+8[/tex]
[tex]6w+L=32[/tex]
Now solve we have the following system of equations
[tex]2w+2L=24[/tex]
[tex]6w+L=32[/tex]
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To solve the system multiply the first equation by -3 and add it to the second equation
[tex]-6w-6L=-72[/tex]
[tex]6w+L=32[/tex]
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[tex]-5L=-40\\\\L=\frac{-40}{-5}\\\\L=8[/tex]
