# 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.

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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.

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
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%