Question

When 5 is subtracted from length and breadth of a rectangle, the perimeter becomes 26. What is the mathematical form of the above statement?​

Answer 1

❍ Let the length of the rectangle be x and breadth be y respectively.

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$\underline{\bigstar\;\boldsymbol{According\;to\;the\;Question:}}$

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• 5 is subtracted from the length and breadth of the rectangle. Therefore,

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★ Length and breadth of the rectangle:

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• Length = (x - 5)
• Breadth = (y - 5)

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

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$\star\;\boxed{\pink{\frak{Perimeter\;_{(rectangle)}=2(Length+Breadth)}}}$

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Therefore,

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$:\implies\sf{26=2\big[\sf{(x-5)+(y-5)\big]}}\\\\\\\\:\implies\sf{26=2(x-5+y-5)}\\\\\\\\:\implies\sf{26=2(x+y-5-5)}\\\\\\\\:\implies\sf{26=2(x+y-10)}\\\\\\\\:\implies\sf{\cancel{\dfrac{26}{2}}=x+y-10}\\\\\\\\:\implies\sf{13=x+y-10}\\\\\\\\:\implies\sf{13+10=x+y}\\\\\\\\:\implies\underline{\boxed{\purple{\frak{x+y=23}}}}{\;\bigstar}$

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$\therefore\;{\underline{\sf{Hence,\;the\;required\;statement\;is\;{\textsf{\textbf{(x\;+\;y)\;=\;23}}}}.}}$⠀⠀⠀