Question

The perimeter of and rectangle plot is 90m and if the length is increased by 3m and breath is decreased by 4m and then area is decreased by 52 m^2. Find the original dimension of the rectangle plot.

Answer 1

$\sf\blue{\underline{\underline{Answer:}}} \\ \\ \sf{The \ dimensions \ of \ the \ rectangle \ are} \\ \sf{25 \ m \ 20 \ m \ respectively.} \\ \\ \sf\orange{Given:} \\ \\ \sf{\leadsto{Perimeter \ of \ a \ rectangle \ plot=90 \ m}} \\ \\ \sf{\leadsto{If \ it's \ length \ is \ increased \ by \ 3 \ m}} \\ \sf{and \ breadth \ is \ decreased \ by \ 4 \ m \ then \ area} \\ \sf{is \ decreased \ by \ 52 \ m^{2}} \\ \\ \sf\pink{To \ find:} \\ \\ \sf{The \ original \ dimensions \ of \ the \ rectangle}$

$\sf\green{\underline{\underline{Solution:}}} \\ \\ \sf{Let \ the \ original \ length \ and \ breadth \ be \ x \ and \ y.} \\ \\ \sf{According \ to \ the \ first \ condition} \\ \\ \boxed{\sf{Perimeter \ of \ rectangle=2(l+b)}} \\ \\ \sf{90=2(x+y)} \\ \\ \sf{\therefore{x+y=45...(1)}} \\ \\ \sf{According \ to \ the \ second \ condition} \\ \\ \sf{(x+3)(y-4)=xy-52} \\ \\ \sf{xy-4x+3y-12=xy-52} \\ \\ \sf{\therefore{4x-3y=40...(2)}} \\ \\ \sf{Multiply \ equation \ (1) \ by \ 3} \\ \\ \sf{3x+3y=135...(3)} \\ \\ \sf{Add \ equations \ (1) \ and \ (2)} \\ \\ \sf{7x=175} \\ \\ \sf{\therefore{x=\dfrac{175}{7}}} \\ \\ \boxed{\sf{x=25}} \\ \\ \sf{Substitute \ x=25 \ in \ equation \ (1)} \\ \\ \sf{25+y=45} \\ \\ \boxed{\therefore{y=20}}} \\ \\ \purple{\tt{\therefore{The \ dimensions \ of \ the \ rectangle \ are}}} \\ \purple{\tt{25 \ m \ and \ 20 \ m \ respectively.}}$