The length of a rectangle is 6 yards more than twice the width. The area of the rectangle is 36 𝑦𝑑2. Find the length.Responses3 yards3 yards8 yards8 yards12 yards12 yards18 yards

Let's denote the width of the rectangle as x (in yards). According to the problem, the length of the rectangle is 6 yards more than twice the width, so we can express the length as 2x + 6.

The area of a rectangle is given by the formula: Area = length * width. In this case, the area is 36 square yards. So we can set up the equation:

36 = (2x + 6) * x

Solving this equation will give us the value of x (the width), and substituting x into the expression for the length will give us the length of the rectangle.

Let's solve the equation:

36 = 2x^2 + 6x 0 = 2x^2 + 6x - 36

Divide the entire equation by 2 to simplify:

0 = x^2 + 3x - 18

This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it by factoring:

0 = (x - 3)(x + 6)

Setting each factor equal to zero gives the solutions x = 3 and x = -6. Since a width can't be negative, we discard x = -6.

So, the width of the rectangle is 3 yards.

Substitute x = 3 into the expression for the length:

Length = 2(3) + 6 = 12 yards.

So, the length of the rectangle is 12 yards.