Question

The length and breadth of a rectangle are given as (6x - 1) and (x -2) metres respectively. If the length and breadth are each increased by 4 metres, the new area is three times that of original rectangle.

1. Form an equation in x and solve it. 
2. Find the dimensions of the original triangle 
3. Express the increase in area as a percentage of the original area. 

Answer 1

1. Form an equation in x and solve it. 
   Dimensions of the new rectangle
   (6x +3) and (x + 2)
   (6x + 3) (x +2) = 6x² + 15x + 6
   = 6x² + 15x +6 = 3 (6x - 1) (x- 2)
   = 6x² + 15x + 6 = 18x2 – 39x + 6
   12x² – 54x = 0
   6x(2x -9) = 0
   2x = 9 x =4.5
2. Find the dimensions of the original triangle 
   Length = 26m
   Breadth = 2.5m
   Original area
   26 x 2.5 = 65m²
    
3. Express the increase in area as a percentage of the original area. 
   New area
   30 x 6.5 = 195m²
   % increase
   = 195-6565×100%
   = 200%