Question

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. However, if the length of this rectangle increases by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Let the length of the rectangle = x units and its breadth = y units

According to first condition :
$(x-5)(y+3)=xy-9$ and

According to second condition:
$(x+3)(y+2)=xy+67$

Answer 1

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