Question

The perimeter of a rectangular plot is 32 metres. If length is increased by 2 metres and breadth is decreased by one metre, the area of the plot remains unchanged. Find the dimensions of the plot.

Answer 1

Answer:

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Step-by-step explanation:

Rectangle

The perimeter =32m

2[L+b]=32m

b+L=16-------Equation 1

area1=length[L]Xbreadth[b]

L2=L+2

b2=b-1

area2=area1

LXb=[L+2][b-1]

Lb=Lb-L+2b-2

2b-L-2=0{Lb is sent that side and Lb-Lb=0}

2b-L=2--------Equation 2

Equation 1 + Equation 2

   b+L=16

{+}2b-L=2

=3b=18

then b=6 breadth of the plot = 6m

length

b+L=16

6+L=16

L=10m

Length of the plot=10m

Answer 2

AnswEr :

$\bf{\green{\underline{\underline{\bf{Given\::}}}}}$

The perimeter of a rectangular plot is 32 metres. If length is increased by 2 metres and breadth is decreased by 1 metres, the area of the plot remains unchanged.

$\bf{\green{\underline{\underline{\bf{To\:find\::}}}}}$

The dimensions of the plot.

$\bf{\green{\underline{\underline{\bf{Explanation\::}}}}}$

Let the length of the plot be r

Let the breadth of the plot be m

$\bf{\boxed{\bf{Area\:of\:rectangle\:=\:Length\times breadth}}}}}$

→ Area = rm

$\bf{We\:have}\begin{cases}\sf{Perimeter\:of\:the\:plot=32\:m}\\ \sf{Length\:of\:the\:plot\:(l)=(r+2)m}\\ \sf{breadth\:of\:the\:plot\:(b)=(m-1)m}\end{cases}}$

$\bf{\red{\underline{\underline{\tt{A.T.Q\::}}}}}$

$\leadsto\sf{2(r+m)=32}\\\\\\\leadsto\sf{r+m=\cancel{\dfrac{32}{2} }}\\\\\\\leadsto\sf{\green{r+m=16........................(1)}}$

Then;

$\leadsto\sf{(r+2)(m-1)=rm}\\\\\\\leadsto\sf{\cancel{rm}-r+2m-2=\cancel{rm}}\\\\\\\leadsto\sf{-r+2m=2}\\\\\\\leadsto\sf{2m=2+r}\\\\\\\leadsto\sf{\red{m=\dfrac{2+r}{2} .....................(2)}}$

Putting the value of m in equation (1), we get;

$\leadsto\sf{r+\dfrac{2+r}{2} =16}\\\\\\\leadsto\sf{\dfrac{2r+2+r}{2} =16}\\\\\\\leadsto\sf{2r+2+r=32}\\\\\\\leadsto\sf{3r+2=32}\\\\\\\leadsto\sf{3r=32-2}\\\\\\\leadsto\sf{3r=30}\\\\\\\leadsto\sf{r=\cancel{\dfrac{30}{3} }}\\\\\\\leadsto\sf{\green{r=10\:m}}$

Putting the value of r in equation (2), we get;

$\leadsto\sf{m=\dfrac{2+10}{2} }\\\\\\\leadsto\sf{m=\cancel{\dfrac{12}{2} }}\\\\\\\leadsto\sf{\green{m=6\:m}}$

$\star\large{\orange{\underline{\sf{The\:dimensions\:of\:the\:plot\::}}}}}}$

• Length = r = 10 m
• Breadth = m = 6 m