Question

The length of a rectangle is 2 inches less than twice its width. the area of the rectangles is 40 square inches find the length and width.

Answer 1

Given

The area of the rectangle is 40 sq inches.

Let the width of a rectangle is x .

The length of a rectangle is 2 inches less than twice its width. 

So the length of  the rectangle is 2 x - 2 .

The area of the rectangle = length * width.

40 = ( 2 x - 2 ) * x

40 =  2 x ^2  - 2 x

2 x ^2  - 2 x - 40 = 0

2 ( x ^2  - x - 20 ) = 0

x ^2  - x - 20 = 0

x ^2 - 5 x + 4 x - 20 = 0

x ( x  - 5 ) + 4 ( x - 5 ) = 0

( x - 5 ) ( x + 4 ) = 0

Apply zero  property.

x - 5 = 0 and x + 4 = 0

x =  5 and x = - 4

Width measurent is always positive.

The width of a rectangle is 5 inches.

Therefore the length of a rectangle is 2 x - 2.

 = 2 ( 5 ) - 2 = 10 - 2  = 8 inches.

Solution :   The length of a rectangle is 8 inches and

the width of a rectangle is 5 inches.