the length of a rectangle is 8 less than twice its width. the area is 42.

Question

The length of a rectangle is 8 less than twice its width. If the area is 42 square units, find the length of the rectangle.

Answer 1

The area of the rectangle is 42 square units.

Let the width of a rectangle is w.

The length of a rectangle is 8 less than twice its width.

So the length of  the rectangle is 2w - 8.

The area of the rectangle = length * width.

42 = ( 2w - 8 ) * w

42 = 2 w ^2 - 8w

2 w ^2 - 8w - 42  = 0.

w ^2 - 4w - 21  = 0.

w ^2 - 7w + 3w - 21  = 0

w ( w - 7 ) + 3 ( w - 7 ) = 0

( w - 7 )  ( w + 3 ) = 0

Zero product rule

w - 7 = 0 and  w + 3  = 0

w = 7  and w = - 3.

Width measurent is always positive.

The length of a width = 7 units.

Therefore the length of a rectangle is 2w - 8.

 = 2 ( 7 )  - 8 = 14  - 8 = 6.

Solution :   The length of a rectangle is 6 units.