Question

answer this question pls its urgent ​

Answer 1

$\sf\blue{Question}$

$\sf{The \ length \ of \ the \ rectangle \ exceeds}$

$\sf{it's \ breadth \ by \ 3 \ cm. \ If \ the \ length}$

$\sf{and \ breadth \ are \ each \ increased \ by \ 2 \ cm, }$

$\sf{then \ the \ area \ of \ the \ new \ rectangle}$

$\sf{will \ be \ 70 \ sq.cm \ more \ than \ that \ of}$

$\sf{the \ given \ rectangle. \ Find \ the \ length}$

$\sf{and \ breadth \ of \ the \ given \ rectangle.}$

___________________________________

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{Length \ and \ breadth \ of \ rectangle}$

$\sf{are \ 18 \ cm \ and \ 15 \ cm \ respectively.}$

$\sf\orange{Given:}$

$\sf{\implies{The \ length \ of \ the \ rectangle \ exceeds}}$

$\sf{it's \ breadth \ by \ 3 \ cm.}$

$\sf{\implies{If \ the \ length \ and \ breadth \ are}}$

$\sf{each \ increased \ by \ 2 \ cm, \ then \ the}$

$\sf{area \ of \ new \ rectangle \ will \ be \ 70 \ cm^{2}}$

$\sf{more \ than \ the \ given \ triangle.}$

$\sf\pink{\underline{\underline{To \ find:}}}$

$\sf{Length \ and \ breadth \ of \ the \ rectangle.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ length \ of \ the \ rectangle \ be \ x}$

$\sf{and \ it's \ breadth \ be \ y.}$

$\sf{According \ to \ first \ condition.}$

$\sf{x=y+3}$

$\sf{\therefore{x-y=3...(1)}}$

$\sf{According \ to \ second \ condition.}$

$\sf{(x+2)(y+2)=xy+70}$

$\sf{xy+2x+2y+4=xy+70}$

$\sf{2x+2y=70-4}$

$\sf{2(x+y)=66}$

$\sf{\therefore{x+y=\frac{66}{2}}}$

$\sf{\therefore{x+y=33...(2)}}$

$\sf{Add \ equations \ (1) \ and \ (2)}$

$\sf{x-y=3}$

$\sf{+}$

$\sf{x+y=33}$

____________________

$\sf{2x=36}$

$\sf{\therefore{x=\frac{36}{2}}}$

$\boxed{\sf{\therefore{x=18}}}$

$\sf{Substitute \ x=18 \ in \ equation (2)}$

$\sf{18+y=33}$

$\sf{\therefore{y=33-18}}$

$\boxed{\sf{\therefore{y=15}}}$

$\sf{\therefore{Length=18 \ cm}}$

$\sf{\therefore{Breadth=15 \ cm}}$

$\sf\purple{\tt{\therefore{Length \ and \ breadth \ of \ rectangle}}}$

$\sf\purple{\tt{are \ 18 \ cm \ and \ 15 \ cm \ respectively.}}$