Question

the area of rectangle gets reduced by 9 square units , if its length is reduced by 5 units and breath is increased by 3 units . if we increase the length by 3 units and breath by 2 units the area increases by 67 square units. find the dimensions of the rectangle . ​

Answer 1

Answer:

let length = x, breadth = y,

(x - 5)(y + 13) = xy -9

xy + 3x - 5y - 15 = xy - 9

3x - 5y = 6

3x = 6 + 5y

x = (6 + 5y)/3 _______ (1)

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

xy + 2x + 3y + 6 = xy + 67

2x + 3y = 61 _______ (2)

substitute (1) into (2), substitute y = 3.77 into (1),

2( (6 + 5y)/3 ) + 3y = 61 x = ( 6 + 5(3.77) )/3

6(6 + 5y) + 9y = 183 x = 24.85/3

36 + 30y + 9y = 183 x = 8.28 units

39y = 147

y = 3.77 units

therefore, length of the rectangle = 8.28 units and the breadth of the rectangle = 3.77 units.