Question

if in a rectangle the length is increased and breadth is reduced each by 2 metre the area is reduced by 28 metre square if the length radius the by one metre and breadth increased by 2 metre area increases by 33 metres square find the length and breadth​

Answer 1

Let the length of the rectangle be "L" Meter and Breadth of the Rectangle be "B" Meter.

now,

The area of a rectangle is equal to  length times its breadth.

$Area = length*breadth\\ \\ \\ Area=LB$

$\rule{200}{2}$

Now,

Case 1 :-

(i)Length is increased by 2 M

(ii)Breadth is reduced by 2 M

thus :-

$(L+2)(B-2)=LB-28\\ \\ \\ LB-2L+2B-4 = LB-28\\ \\ \\2B-2L=4-28=(-24)\\ \\ \\B-L=\dfrac{-24}{2}=(-12)$

$\rule{200}{2}$

Case 2:-

(i)Length is reduced by 1M

(ii)Breadth is increased by 2 M

Hence:-

$(L-1)(B+2)=LB+33\\ \\ \\LB+2L-B-2=LB+33\\ \\ \\2L-B=33+2=35$

$\rule{200}{2}$

$\rule{200}{2}$

We have two equations:-

solving the two equations :-

$-L+B=(-12)\\2L-B=35\\============\\L=23\\ \\ \\B=L-12=23-12=11$

$\rule{200}{2}$

Length = 23 M

Breadth=11 M

Answer 2

Step-by-step explanation:

Let the length of the rectangle be "L" Meter and Breadth of the Rectangle be "B" Meter.

now,

The area of a rectangle is equal to length times its breadth.

$\begin{lgathered}Area = length*breadth\\ \\ \\ Area=LB\end{lgathered}$

Now,

Case 1 :-

(i)Length is increased by 2 M

(ii)Breadth is reduced by 2 M

thus :-

$\begin{lgathered}(L+2)(B-2)=LB-28\\ \\ \\ LB-2L+2B-4 = LB-28\\ \\ \\2B-2L=4-28=(-24)\\ \\ \\B-L=\dfrac{-24}{2}=(-12)\end{lgathered}$

Case 2:-

(i)Length is reduced by 1M

(ii)Breadth is increased by 2 M

Hence:-

$\begin{lgathered}(L-1)(B+2)=LB+33\\ \\ \\LB+2L-B-2=LB+33\\ \\ \\2L-B=33+2=35\end{lgathered}$

We have two equations:-

solving the two equations :-

$\begin{lgathered}-L+B=(-12)\\2L-B=35\\============\\L=23\\ \\ \\B=L-12=23-12=11\end{lgathered}$

Length = 23 M

Breadth=11 M