Question

The area of rectangle get reduced by 9 square units, if its length is reduced by 5 units and breadth is reduced by 3units. If we increase the length by 3 and the breadth by 2 units, the area increase by 67 square units. Find the dimensions of rectangle. Solve it by cross multiplication method.​

Answer 1

Answer:

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Step-by-step explanation:

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.

Answer 2

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.