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.

Question

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :

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.

Answer 1

Length of rectangle is ‘x’ unit.

Breadth of rectangle is ‘y’ unit.

Area of rectangle = length × breadth = xy

(x – 5) (y + 3) = xy – 9 

xy + 3x – 5y – 15 = xy – 9 

3x – 5y = -9 + 15 

3x – 5y = 6 …………. (i) 

(x + 3) (y + 2) = xy + 67 

xy + 2x + 3y + 6 = xy + 67 

2x + 3y = 67 – 6 

2x + 3y = 61 ……….. (ii) 

Solving the equation by Elimination method : 

Multiplying eqn. (i) by and eqn. (ii) by 5 

9x – 15y = 18 ………….. (iii) 

10x + 15y = 305 ………… (iv) 

From eqn. (iii) + eqn. (iv)

∴ x = 17 unit. 

Substituting the value of ‘x’ in eqn. (i), 

3x – 5y = 6 

3(17) – 5y = 6 

51 – 5y = 6 

-5y = 6 – 51 – 5y = – 45 

5y = 45

∴ y = \(\frac{45}{5}\) 

∴ y = 9 units. 

∴ Length of that rectangle, x = 17 unit breadth, y = 9 unit.