Question

the length of a rectangular field is 8 metre less than twice its breadth if the perimeter of a rectangular field is 80 meters
find its length and breadth​

Answer 1

❍ Let's say, that the breadth of the field be x and length of the field be (2x - 8) respectively.

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$\underline{\bf{\dag\;}\frak{As\;we\;know\;that:}}$

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$\star\;\boxed{\pink{\sf{Perimeter_{(rectangle)}=2(L+B)}}}$

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Therefore,

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$\begin{gathered}:\implies\sf{2\;(2x-8+x)=80}\\\\\\\\:\implies\sf{2(3x-8)=80}\\\\\\\\:\implies\sf{3x-8=\cancel{\dfrac{80}{2}}}\\\\\\\\:\implies\sf{3x-8=40}\\\\\\\\:\implies\sf{3x=40+8}\\\\\\\\:\implies\sf{3x=48}\\\\\\\\:\implies\sf{x=\cancel{\dfrac{48}{3}}}\\\\\\\\:\implies\underline{\boxed{\frak{\pink{x=16\;m}}}}\;\bigstar\end{gathered}$

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Hence,

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• Breadth = x = 16m
• Length = (2x - 8) = 2(16) - 8 = (32 - 8) = 24m

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$\therefore\;{\underline{\sf{Hence,\;the\;length\;and\;breadth\;of\;the\;field\;are\;{\textsf{\textbf{16\;m}}}\;\&\;{\textsf{\textbf{24\;m}}}}.}}$⠀⠀