Question

A rectangular vegetable garden will have a width that is four feet less than the length, and an area of 140 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 __________ feet.

Answer 1

x = 14

Explanation:

Given the following values for the rectangular vegetable garden:

x = length

(x - 4) = width

140 = area of the rectangular vegetable garden

To solve for the length of the garden, start by distributing x into the parenthesis:

x ( x - 4 ) = 140

x² - 4x = 140

Subtract 140 from both sides:

x² - 4x - 140 = 140 - 140

x² - 4x - 140 = 0

where a = 1, b = -4, and c = -140

Next, substitute the values for a, b, and c into the quadratic formula:

`x = \frac{-b +/- \sqrt{b^(2)-4ac} }{2a}`

`x = \frac{4 +/- \sqrt{(-4)^(2)-4(1)(-140)} }{2(1)}`

`x = (4 +/- √(16+560) )/(2)`

`x = (4 +/- √(576) )/(2)`

`x = \frac{4 +/- \sqrt{24^(2) } }{2}`

`x = (4+24)/(2)` ,
`x = (4-24)/(2)`

x = 14, x = -10

Given these two values for x, let's test each of them to see which value will provide a true statement:

x = 14

14( 14 - 4 ) = 140

14(10) = 140

140 = 140 (True statement).

x = -10

-10( -10 - 4 ) = 140

-10(-14) = 140

140 = 140 (True statement).

Even though both values for x provided a true statement, it wouldn't make sense to have a negative value for the length of a rectangular garden. Therefore, the correct answer is x = 14.