Question

Gerald purchases a rectangle plot of land The length of the plot is 20 feet more than the width. The cost of the land was $12 per square foot. Gerald also had a fence put around the entire perimeter of the plot, at a cost of $8 per linear foot. The total amount he spent on both the land and the fence was $10,560.

Write an equation in one variable that can be used to find the width, x feet, of the plot. Express the equation in the form ax^2 + bx + c = 0. Provide evidence to support your answer.

Answer 1

`12x^(2)+272x+320=10560`

Explanation:

Start by setting the width = x.

Length is equal to x+20.

We know the cost of the land was $12 per square foot (area) and the cost of the fence around the perimeter is equal to $8 per foot. This gives us two equations we need to work with.

$12(x*(x+20)) + $8((2*x)+(2*(x+20))) = 10560. It looks a little difficult to read but as we distribute the cost throughout the equations, we see it start to take shape.

12(x^2+20x) + 8(2x+2x+40) = 10560

12x^2+240x+16x+16x+320 = 10560

12x^2+272x+320=10560

The roots of our equation here are x=20, and x = -128/3

Since we know that area is not negative, our answer is x=20.

Check the work: 12(20)^2 + 272(20) +320 = 10560