Question

The perimeter of a rectanglar plot is 32mt. If the length is increased by 2m and the breadth is

decreased by 1mt. The area of the plot remains the same. Find the length and breadth of the plot​

Answer 1

Answer:

l=10 and b=6

Step-by-step explanation:

let length be l and breadth be b

now,2(l+b)=32

l+b=16{equation1}

area=lb

according to question.

(l+2)(b-1)=lb

lb-l+2b-2=lb

-l+2b=2

add 3l to both sides

2l+2b=2+3l

2(l+b)=2+3l

2(16)=2+3l

2+3l=32

3l=30

l=10

and l+b=16

b=6

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Answer 2

Solution :

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

The perimeter of a rectangle plot is 32 m. If the length is increased by 2 m and the breadth is decreased by 1 m. The area of the plot remains the same.

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

The length and breadth of the plot.

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

Let the length of the plot be r m

Let the breadth of the plot be m m

Formula use :

$\bf{\boxed{\sf{Perimeter\:of\:rectangle=2(length+breadth)}}}}}$

A/q

$\implies\tt{2(r+m)=32}\\\\\implies\tt{r+m=\cancel{\dfrac{32}{2} }}\\\\\implies\tt{\red{r+m=16............................(1)}}$

&

$\bf{\boxed{\sf{Area\:of\:rectangle=(length\times breadth)}}}}}$

$\implies\tt{(r+2)(m-1)=rm}\\\\\implies\tt{\cancel{rm}-r+2m-2=\cancel{rm}}\\\\\implies\tt{-r+2m-2=0}\\\\\implies\tt{-r+2m=2}\\\\\implies\tt{2m=2+r}\\\\\implies\tt{\green{m=\dfrac{2+r}{2}...................(2) }}$

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

$\implies\tt{r+\dfrac{2+r}{2} =16}\\\\\\\implies\tt{\dfrac{2r+2+r}{2} =16}\\\\\\\implies\tt{2r+2+r=32}\\\\\\\implies\tt{3r+2=32}\\\\\\\implies\tt{3r=32-2}\\\\\\\implies\tt{3r=30}\\\\\\\implies\tt{r=\cancel{\dfrac{30}{3} }}\\\\\\\implies\tt{\red{r=10\:m}}$

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

$\implies\tt{m=\dfrac{2+10}{2} }\\\\\\\implies\tt{m=\cancel{\dfrac{12}{2} }}\\\\\\\implies\tt{\red{m=6\:m}}$

Thus;

$\underbrace{\sf{The\:length\:of\:the\:plot\:=r=10\:metres}}}}}}\\\underbrace{\sf{The\:breadth\:of\:the\:plot\:=m=6\:metres}}}}}}$