Question

Two less than three times the width of a rectangle is equal to the length. The area of the rectangle is 65 square ft. What is the length of the rectangle?

Answer 1

The length of this beautiful, significant shape is 2.

Answer 2

Answer:

Length of the rectangle = 13 ft

Step-by-step explanation:

Let l be the length and w be the width of this rectangle.

Two less than three times the width of a rectangle is equal to the length, that is

          3w - 2 = l---------------------------eqn 1

The area of the rectangle is 65 square ft

          l x w = 65  

Substituting eqn 1

           (3w - 2) x w = 65

            3w² - 2w -65 = 0

Solving quadratic eqn

            $w=\frac{-(-2)\pm \sqrt{(-2)^2-4\times 3\times (-65)}}{2\times 3}=\frac{2\pm \sqrt{4+780}}{6}\\\\w=\frac{2\pm \sqrt{784}}{6}\\\\w=\frac{2\pm 28}{6}\\\\w=\frac{2+28}{6}\texttt{ or }w=\frac{2-28}{6}\\\\w=5\texttt{ or }w=-4$

w cannot be negative

Hence width, w = 5 ft

Substituting in eqn 1

              3 x 5 - 2 = l

             l = 13 ft

Length = 13 ft

Length of the rectangle = 13 ft