Question

The length of a rectangle is 1 less than twice the width.

The area of the rectangle is 28 square feet.

Which equation represents the situation?

What is the length of the rectangle?

Answer 1

`w-width\\2w-1-length\\w(2w-1)=2w^2-w-the\ area\\28\ ft^2-the\ area\\\\\text{The equation:}\\\\2w^2-w=28\qquad\text{subtract 28 from both sides}\\\\2w^2-w-28=0\\\\2w^2-8w+7w-28=0\\\\2w(w-4)+7(w-4)=0\\\\(w-4)(2w+7)=0\iff w-4=0\ \vee\ 2w+7=0\\\\w-4=0\qquad\text{add 4 to both sides}\\\boxed{w=4}\\\\2w+7=0\qquad\text{subtract 7 from both sides}\\2w=-7\qquad\text{divide both sides by 2}\\w=-3.5<0\\\\\text{The length:}\ 2(4)-1=8-1=7\\\\Answer:\ \boxed{\text{The length is equal 7\ ft}}`

Answer 2

equation = 2w^2- w- 28 =0

length =7