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

Answer 1

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