Question

A plot of land for sale has a width of x ft., and a length that is 6ft less than its width. A

farmer will only purchase the land if it measures 352 square feet. What value of x will
cause the farmer to purchase the land?

Answer 1

The final value for the width (x) of the land is 22 feet. This ensures that the area meets the farmer's requirement of 352 square feet, considering the given relationship between the width and length of the land.

Let's denote the width of the land as x feet. According to the given information, the length of the land is x - 6 feet.

The area of the land is given by the product of its length and width, and it should be equal to 352 square feet:

Area = Length × Width

So, we have the equation:

x * (x - 6) = 352

Now, let's solve this equation for x:

x^2 - 6x = 352

x^2 - 6x - 352 = 0

Now, we can factor the quadratic equation or use the quadratic formula to find the values of x. Factoring might not be straightforward in this case, so let's use the quadratic formula:

`\[ x = (-b \pm √(b^2 - 4ac))/(2a) \]`

Here, a = 1, b = -6, and c = -352.

`\[ x = (6 \pm √((-6)^2 - 4(1)(-352)))/(2(1)) \]`

`\[ x = (6 \pm √(36 + 1408))/(2) \]`

`\[ x = (6 \pm √(1444))/(2) \]`

`\[ x = (6 \pm 38)/(2) \]`

Now, we have two possible solutions:

1. x = (6 + 38)/2 = 44/2 = 22

2. x = (6 - 38)/2 = -32/2 = -16

Since the width of the land cannot be negative, we discard the second solution. Therefore, the final value for x is 22 feet.