The width of a rectangle is 30 meters less than triple the length, and the area of the rectangle is 12 M squared. What is the length and width of the rectangle?

Answer 1

L x W = Area of a Rectangle

W = 3L - 30

L(3L - 30) = 12 sq m

3LL - 30L = 12

3LL - 30L - 12 = 0

DIVIDE entire equation by 3, or MULTIPLY by 1/3, or factor out a 3. All accomplish the same result.

LL - 10L - 4 = 0

COMPLETE THE SQUARE!

1/2 of (-10) squared = (-5)(-5) = 25

LL - 10L = 4

LL - 10L + 25 = 4 + 25

LL - 10L + 25 = 29

(L - 5) (L - 5) = 29

EXTRACT SQUARE ROOT FROM BOTH SIDE SIDES

L - 5 = SQUARE ROOT OF 29

L = SQUARE ROOT OF 29 + 5

L = 5.385 + 5 = 10.385 m

W = 3L - 30 = (3) (10.385) - 30 = 31.155 - 30 = 1.155M

THEREFORE, LENGTH=10.385 meters and

WIDTH = 1.155 meters

CHECKING:

Length X Width = (10.385 m) (1.155 m) = 11.99 sq m