Answer:
Option C - 13 feet.
Step-by-step explanation:
Given : Two less than three times the width of a rectangle is equal to the length. The area of the rectangle is 65 square ft.
To find : What is the length of the rectangle?
Solution :
The area of the rectangle is given by,
[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]
The area of the rectangle is 65 square ft.
Let the width of the rectangle be 'w'.
Two less than three times the width of a rectangle is equal to the length.
The length of the rectangle is l=3w-2
Substitute the value in the formula,
[tex]65=(3w-2)\times w[/tex]
[tex]65=3w^2-2w[/tex]
[tex]3w^2-2w-65=0[/tex]
Applying quadratic formula,
[tex]w=\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(65)}}{2(3)}[/tex]
[tex]w=\frac{2\pm\sqrt{4+780}}{6}[/tex]
[tex]w=\frac{2\pm\sqrt{784}}{6}[/tex]
[tex]w=\frac{2\pm28}{6}[/tex]
[tex]w=\frac{2+28}{6},\frac{2-28}{6}[/tex]
[tex]w=\frac{30}{6},\frac{-26}{6}[/tex]
[tex]w=5,-4.33[/tex]
The width of the rectangle is 5 ft.
The length of the rectangle is l=3w-2=3(5)-2=13 ft
Therefore, Option C is correct.
