Find the value of x for the area of the triangle that is 12cm sq. The base is 2x+2 and the height is x.

Solve this equation:
(1/2)(base)(height) = (x+1)x = 12
x^2 + x -12 = 0
That equation is factorable. Take the positive root. (One of them will be negative0

To find the value of x for the area of the triangle, we need to solve the equation (1/2)(base)(height) = 12.

Given that the base is 2x+2 and the height is x, we can substitute these values into the equation:

(1/2)(2x+2)(x) = 12

Now we can simplify the equation:

x(x+1) = 12

Expanding further:

x^2 + x = 12

Rearranging the equation:

x^2 + x - 12 = 0

This is a quadratic equation in standard form. To solve it, we need to factor it. The equation factors as:

(x+4)(x-3) = 0

From this equation, we can see that two possible values of x are -4 and 3. However, since we are dealing with the length of a side, x cannot be negative, so x = 3 is the valid solution.

Hence, the value of x for the area of the triangle is 3 cm.