Question

The length of a rectangular driveway is five feet more than three times the width. The area is 50 square feet. Find the length and width of the driveway.

Short answer

The length of rectangular driveway is 15 feet and the width is 3.3 feet.

Step-by-step solution

Step 1. Given information

The area of a rectangular driveway is 50 square feet . Its length is five feet more than three times the width.

Find the length and width.

Step 2. Calculation

Consider width of the rectangle is x. So length of the rectangle is $3x+5$.

Area of rectangle is 50 square feet.

So, the equation becomes $50=x\left(3x+5\right)$.

Form the quadratic equation.

$3x^2+5x-50=0$

Step 3. Solve the equation

Solve the quadratic equation

$$\begin{gathered} 3x^2+15x-10x-50=0 \\ 3x\left(x+5\right)-10\left(x+5\right)=0 \\ \left(x+5\right)\left(3x-10\right)=0 \end{gathered}$$

Use the Zero Product Property

$x+5=0\Rightarrow x=-5$

$3x-10=0\Rightarrow x=\frac{10}{3}$

Distance can not be negative.

localid="1646052487100" $x=3.3$

Step 4. Conclusion

As width is 3.3 feet,

So length is$\left(3\times 3.3\right)+5=14.9\approx 15$