Question

The area of a rectangle gets reduced by 15 square units if its length is reduced by 6 units and breadth is increased by 2 units. If its length increased by 3 units and breadth by 4 units, the area is increased by 96 square units. Find the length and breadth of the rectangle.​

Answer 1

Solution :-

Let length and breadth of rectangle be x unit and y unit.              

Area = xy    

             

According to the question,                  

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

⇒ 3x - 5y - 6 = 0 ... (i)                  

⇒ (x + 3) (y + 2) = xy + 67                  

⇒ 2x - 3y – 61 = 0 ... (ii)                  

By cross multiplication, we get                  

⇒ x/305 - (-18) = y/-12 -(-183) = 1/9 - (-10)                  

⇒ x/323 = y/171 = 1/19                  

⇒ x = 17, y = 9        

         

Length of the rectangle = 17 units.

Breadth of the rectangle = 9 units.

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Answer 2

Answer:

Let the length and breadth of the rectangle be x and y units respectively. Then,

Area =xy sq. units.

If length is reduced by 5 units and the breadth is increases by 3 units, then area is reduced by 9 square units.

∴xy−9=(x−5)(y+3)

⇒xy−9=xy+3x−5y−15

⇒3x−5y−6=0 ...(i)

When length is increased by 3 units and breadth 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 ...(ii)

Thus, we get the following system of linear equations:

3x−5y−6=0

2x+3y−61=0

By using cross-multiplication, we have

$\frac{x}{305 + 18} = \frac{ - y}{ - 183 + 12} = \frac{1}{9 + 10} \\ x = \frac{323}{19} = 17and \: y = \frac{171}{19} = 9$

Hence, the length and breadth of the rectangle are 17 units and 9 units respectively.