Macarena has a square of cardboard with a side of 10 cm. How many centimeters of cardboard does Macarena have in that square? If she wants to cut a corner in the shape of a right triangle, and the remaining area is 90 square cm, where can she make the cuts?

To find the total length of cardboard in the square, we need to calculate the perimeter. Since it is a square, all sides are equal in length. The formula for the perimeter of a square is given by:
$$\text{Perimeter} = 4 \times \text{side length}$$

Given that the side length of the square is 10 cm, we can substitute this value into the formula to find the perimeter:
$$\text{Perimeter} = 4 \times 10 = 40 \text{ cm}$$

So Macarena has 40 cm of cardboard in that square.

Now let's determine where she can make the cuts to create a right triangle.

Let's assume she cuts out a square corner with length x. The remaining shape will be a rectangle with dimensions (10-x) cm by (10-x) cm. The area of the rectangle is given by multiplying the length and width:
$$\text{Area of rectangle} = (10-x) \times (10-x)$$

Given that the remaining area is 90 square cm, we can set up the following equation:
$$(10-x) \times (10-x) = 90$$

Expanding this equation, we get:
$$100 - 20x + x^2 = 90$$

Rearranging the equation and simplifying further, we have:
$$x^2 - 20x + 100 - 90 = 0$$
$$x^2 - 20x + 10 = 0$$

This is a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

For our equation, a = 1, b = -20, and c = 10. Substituting these values into the quadratic formula, we get:
$$x = \frac{-(-20) \pm \sqrt{(-20)^2 - 4(1)(10)}}{2(1)}$$
$$x = \frac{20 \pm \sqrt{400 - 40}}{2}$$
$$x = \frac{20 \pm \sqrt{360}}{2}$$
$$x = \frac{20 \pm 6\sqrt{10}}{2}$$
$$x = 10 \pm 3\sqrt{10}$$

From the equation, we see that Macarena can make the cuts at x = 10 + 3√10 cm or x = 10 - 3√10 cm.

Answer: Macarena has 40 cm of cardboard in that square, and she can make the cuts at either x = 10 + 3√10 cm or x = 10 - 3√10 cm.