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Q.

The area of a rectangle gets reduced by


9 Square units in its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the


area is increased by 67 sq. units. Find the length and breadth of the rectangle.


Class:  Grade 9


Subiect : Mathematics


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a

17 and 10

b

17 and 9

c

17 and 39

d

None of these  

answer is B.

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Detailed Solution

Let the length and breadth of the rectangle be x and y units respectively. Then,
Area = xy Square units
If length  is  reduced by 5 units and the breadth is increased by 3 units then the area is  reduce by 9 square units
.: xy-9=(x-5)(x+3)
  xy-9=xy+3x-5x-15
When length is increased by 3 unit  and broadth by 2 units, the area is increased by 67 sq.units          xy +67 =(x+3)(y+2)
 xy +67 =xy+2x+3y+6
 2x +3y-61= 0
Thus, we get the following system of linear equations.
3x-5y-6=0
 2x+3y-61=0
By using cross-multiplication, we have
x305+18 = -y-183+12= 19+10
x=32319 =17 and y=17119=9
   
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The area of a rectangle gets reduced by 9 Square units in its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 sq. units. Find the length and breadth of the rectangle. Class:  Grade 9 Subiect : Mathematics