A gardener wants to create a triangular garden in the shape of a right triangle with shortest side length x-2y ft. and the middle length side x+6y ft. What is the area of the garden? multiply this out and express in simpliest correct mathematical form including units

To find the area of the triangular garden, we can use the formula for the area of a triangle: A = (1/2) * base * height.

In this case, the shortest side length (x-2y ft.) will be the base of the triangle, and the middle length side (x+6y ft.) will be considered as the height.

So, the area of the garden can be calculated as:

A = (1/2) * (x-2y) * (x+6y)

Now, let's multiply this out and simplify it:

A = (1/2) * (x^2 + 6xy - 2xy - 12y^2)

A = (1/2) * (x^2 + 4xy - 12y^2)

A = (1/2)x^2 + 2xy - 6y^2

Therefore, the area of the garden is (1/2)x^2 + 2xy - 6y^2 square feet.