Question

Good evening



Form the pair of linear equatioms in the following problem and find the solution by an algebric method.

The area of a rectangle gets reduced by 9sq 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 uniys. Fimd the dimentions of the rectangle. ​

Answer 1

Area of Rectangle = l × b

Case 1:

(l × b) - 9 sq.ut = (l - 5) × (b + 3)

lb - 9 = lb + 3l - 5b - 15

3l - 5b = 6 -------(i)

Case 2:

(l + 3) × ( b + 2) = (l × b) + 67

lb + 2l + 3b + 6 = lb + 67

2l + 3b = 61 --------(ii)

Multiply 2 in equation (i)

2 × (3l - 5b = 6)

6l - 10b = 12 -------(iii)

Multiply 3 in equation (ii)

3 × ( 2l + 3b = 61)

6l + 9b = 183 --------(iv)

Subtract equation (iv) from (iii)

(6l - 10 b) - (6l + 9b) = 12 - 183

6l - 10b - 6l - 9b = -171

-19b = -171

b = 9 ✓

Substitute value of 'b' in equation (i)

3l - 5(9) = 6

3l - 45 = 6

3l = 51

l = 17 ✓

Hence, The value of b = 9units and value of l = 17units.