The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Can you do this question by Elimination Method??

We know that the area of rectangle is of the form xy where length=x and breadth=y

Now according to QUESTION,

(x-5)(y+3)=xy-9--(i)

(x+3)(y+2)=xy+67---(ii)

On solving the 2 equations,we get

- xy+3x-5y-15=xy-9

-->3x-5y=6--(iii)

- xy+2x+3y+6=xy+67

-->2x+3y=61(iv)

** NOW BY ELIMINATION METHOD,**

6x-10y=12(v)

6x+9y=183(vi)

On subtracting (vi) from (v),we get

-19y=-171

=> y=9

On substituting y=9 in (vi),we get

6x+81=183

=> 6x=102 (6x+9y=183 where y=9 is substituted in this equation)

So, x=17

**Therefore,the dimensions of the rectangle are:**

- Length(x)=17 units
- Breadth(y)=9 units

Hope this is clear to you and you would a good idea of how to solve this word problem.

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