Question

A landscaper designs a garden border to run along the inside perimeter of a piece of property that is shaped like a

rectangle.
The garden border that runs along the edge of the property has a width of x meters and surrounds the entire
property. The area inside of the garden border has a width of 39 meters and a length of 21 meters as shown by the
diagram.
The total area of the property, in square meters, is a function of the distance, x, in meters.
Enter the quadratic function, A(x), in standard form that represents the total area of the property in square meters.
If your answer includes exponents, use the symbol. For example, if your answer is 42, enter it like this: 4344

please help me

Answer 1

A = 4x^2 + 120x

Explanation:

(39+2x)(21+2x)-(39*21) = 819 + 78x + 42x + 4x^2 - 819

A = 4x^2 + 120x

Answer 2

The quadratic function A(x) representing the total area of the property including the garden border is A(x) = 4x² + 120x, where x is the width of the garden border in meters.

The student is asking to find a quadratic function A(x), which represents the total area of a property in square meters, where a garden border with a width of x meters runs along the inside perimeter of the rectangular property. Given the inner dimensions of the area surrounded by the garden, which are 39 meters and 21 meters, the total length and width of the property would each be increased by 2x meters (since the border runs along all sides). The total length and width of the property would therefore be (39 + 2x) and (21 + 2x) respectively.

To find the area of the rectangle, we multiply the length by the width: A(x) = (39 + 2x) × (21 + 2x)

Expanding this, we attain: A(x) = 819 + 78x + 42x + 4x²

Combining like terms: A(x) = 4x² + 120x + 819

Since the question requires the area of the property in the form of A(x) = 4x² + 120x, the constant term (819, which represents the area of the inner rectangle) is not included in the function form requested by the student. Therefore, the final answer is: A(x) = 4x² + 120x