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? a 9 feet b 11 feet c 13 feet d 20 feet

Explanation:

Step1: Let the width be $w$.

The length $l = 3w - 2$.

Step2: Recall area formula.

The area of a rectangle $A=l\times w$, and $A = 65$. So, $(3w - 2)\times w=65$.

Step3: Expand the equation.

$3w^{2}-2w - 65=0$.

Step4: Factor the quadratic - equation.

$3w^{2}-15w + 13w-65 = 0$, $3w(w - 5)+13(w - 5)=0$, $(3w + 13)(w - 5)=0$.

Step5: Solve for $w$.

We get $w = 5$ or $w=-\frac{13}{3}$. Since width cannot be negative, $w = 5$.

Step6: Find the length.

Substitute $w = 5$ into the length formula $l=3w - 2$, $l=3\times5 - 2=13$.

Answer:

C. 13 feet