Question

The perimeter of a rectanglar plot is 32mt. If the length is increased by 4m 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

$\huge\boxed{\fcolorbox{blue}{orange}{HELLO\:MATE}}$

GIVEN:

→Perimeter of a regtangular plot is 32m

→If the length is increased by 4m and the breadth is decreased by 1mt. The area of the plot remains the same.

TO FIND:

→The length and the breadth of the plot.

SOLUTION:

let's take the length be 'l' and the breadth be 'b'.

FIRST CASE:

Length = l

Breadth= b

So, perimeter =2(l+b)

$\large\red{\boxed{Perimeter=2(length+breadth)}}$

=>$2(l+b) =32m$

=>$(l+b) =\dfrac{32m}{2}$

=>$l+b=16m$ ................. (1)

Now, Area =lb

$\large\green{\boxed{Area=lenght×breadth}}$

______________________________________

SECOND CASE:

Length= (l+4) m

Breadth=(b-1) m

So,Area= lenght×breadth

=$(l+4) (b-1)$

________________________________

Atq,

=>$(l+4) (b-1) = lb$

=>$(l+4) (16-l-1) =l(16-l)$

(from equation 1)

=>$(l+4)(15-l) =16l-l^{2}$

=>$15l +60-l^{2}-4l =16l-l^{2}$

=>$-16l + 15l -4l =-60$

=>$-5l =-60$

=>$l =\dfrac{-60}{-5}$

=>$l = 12m$

Therefore length of the plot is 12m

From......... 1,we have,

=>$l+b=16m$

=>$12m + b =16m$

=>$b =(16-12) m$

=>$b = 4m$

Therefore breadth of the plot is 4m

$\huge\blue{\boxed{Lenght=12m}}$

$\huge\blue{\boxed{Breadth=12m}}$

Answer 2

Answer:

xy=xy-x+2y-2

x=2y-2

the Peri. of rect. is 32

so, perimeter=32

2(l+b)=32

2(x+y)=32

x+y=16

2y-2+y=16

3y=18

y=6

when y=6,then,x=10

means length=10,breadth=6.

Step-by-step explanation:

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