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. 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??

Answer 1

Let length of rectangle = x units

And width of rectangle = y units

Area of rectangle = length * width = x*y

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.

So

Decrease the length by 5 unit so new length = x - 5

Increase the width by 3 unit so new width = y + 3

New area is reduced by 9 units

So new area  = xy – 9

Plug the value in formula length * width = area we get

(x  - 5)(y + 3) = xy  - 9

Xy  + 3x – 5y – 15  = xy – 9

Subtract xy both side we get

3x - 5y  = 6                 …(1)

If we increase the length by 3units and the breadth by 2 units, the area increases by 67 square units.

Increase the length by 3 unit so new length = x +3

Increase the width by 2 unit so new width = y + 2

New area is increased  by 67 units

So new area  = xy + 67

Plug the value in formula length * width = area we get

(x  +3)(y + 2) = xy  +  67

Xy  + 2x  +  3y  +  6  = xy + 67

Subtract xy both side we get

2x  +  3y = 61                         …(2)*3

3x - 5y  = 6                 …(1)*2

Cross multiply the coefficient of x we get

6x + 9 y = 183

6x -10y  =12

Subtract now we get

19 y = 171

Y = 171/19 = 9

Plug this value of y in equation first we get

2x + 3* 9 = 61

2x  = 61 – 27

2x = 34

X = 34/2 = 17

So length is 17 units and width is 9 units

Answer 2

Answer:

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.