The length of the rectangle is 3times its width. If its length in increased by 2 meter and its width decrease is 1meter the area of the new rectangle is 68square meter. Find the dimension of the original rectangle
L = length
W = width
The length of the rectangle is 3 times its width means:
L = 3 W
If its length in increased by 2 meter and width decrease is 1 meter new dimensions are:
3 W + 2
and
W - 1
The new rectangle is 68 m² means:
( 3 W + 2 ) ∙ ( W - 1 ) = 68
3 W ² + 2 W - 3 W - 2 = 68
3 W ² - W - 2 = 68
Subtract 68 to both sides.
3 W ² - W - 70 = 0
The solutions are:
W = - 14 / 3 and W = 5
Width cannot be negative therefore:
W = 5
L = 3 W = 3 ∙ 5
L = 15
The dimension of the original rectangle:
length
L = 15 m
W = 5 m
Check result:
If length increased by 2 meter and width decrease is 1 meter new dimensions are:
15 m + 2 m = 17 m
and
5 m - 1 m = 4 m
17 m ∙ 4 m = 68 m²