Question

A rectangular garden is 21 feet long and 14 feet wide. A brick walk way with uniform width is going to be constructed around the garden. The brick walk way will have an area of 330 square feet. What should be the width of the brick walk way? Type in your answer to the nearest thousandth. The width of the walk way should be?

Answer 1

Answer:

3.862 feet

Explanation:

Let the uniform width of the walkway = x ft

From the diagram above, the area of the walkway will be:

$2x(21+2x)+2(14x)$

The brick walkway will have an area of 330 square feet. Therefore:

$2x(21+2x)+2(14x)=330$

We simplify the equation in order to solve for x:

$\begin{gathered} 42x+4x^2+28x=330 \\ 4x^2+28x+42x-330=0 \\ 4x^2+70x-330=0 \end{gathered}$

Next, solve for x:

$\begin{gathered} 2(2x^2+35x-165)=0 \\ 2x^2+35x-165=0 \end{gathered}$

Using the quadratic formula, we solve for x:

$\begin{gathered} x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\ x=\dfrac{-35\pm\sqrt{35^2-4(2)(-165)}}{2\times2} \\ =\dfrac{-35\pm\sqrt{1225-(-1320)}}{4} \\ =\dfrac{-35\pm\sqrt{2545}}{4} \\ x=\frac{-35+\sqrt{2545}}{4}\text{ or }x=\frac{-35-\sqrt{2545}}{4} \\ x=3.862\text{ or }x=-21.362 \end{gathered}$

The width of the brick walkway should be 3.862 feet (correct to the nearest thousandth).