Question

A rectangular vegetable garden will have a width that is 4
feet less than the length, and an area of 140
square feet. If x represents the length, then the length can be found by solving the equation:
x(x-4)=140

What is the length, x, of the garden?

The length is blank feet.

Answer 1

To find the length \( x \) of the garden, we can solve the equation given:

\[
x(x - 4) = 140
\]

First, expand the left side:

\[
x^2 - 4x = 140
\]

Next, move all terms to one side of the equation to set it to zero:

\[
x^2 - 4x - 140 = 0
\]

Now we can use the quadratic formula to solve for \( x \). The quadratic formula is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In our equation, \( a = 1 \), \( b = -4 \), and \( c = -140 \).

We calculate the discriminant:

\[
b^2 - 4ac = (-4)^2 - 4(1)(-140) = 16 + 560 = 576
\]

Now plug the values into the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{576}}{2(1)}
\]
\[
x = \frac{4 \pm 24}{2}
\]

This gives us two possible solutions for \( x \):

1. \( x = \frac{4 + 24}{2} = \frac{28}{2} = 14 \)
2. \( x = \frac{4 - 24}{2} = \frac{-20}{2} = -10 \)

Since a length cannot be negative, we discard \( -10 \) as a solution.

Thus, the length \( x \) of the garden is:

\[
\boxed{14} \text{ feet.}
\]