When a square of area 4 is dilated by a scale factor of k, we obtain a square of area 9. Find the sum of all possible values of k.

I do not understand...it is not 3/2, as I was told, but I don't understand why? Help?

4*k = 9

k = 9/4

(9/4) * 4 = 9.

burma is this problem?

To find the sum of all possible values of k, we need to set up an equation based on the given information.

Let's start by considering the area of the original square, which is 4. Since the side length of a square is equal to the square root of its area, we can say that the side length of the original square is √4 = 2.

When this original square is dilated by a scale factor of k, the dimensions of the new square are changed. Let's denote the side length of the new square as x.

We are given that the area of the new square is 9. Using the formula for the area of a square (A = side length squared), we can write the equation:

x^2 = 9

Taking the square root of both sides of the equation, we get:

x = √9 = 3

So, the side length of the dilated square is 3.

Now, we can relate the side lengths of the original and dilated squares using the scale factor k. The ratio of the side lengths is given by:

k = x / 2

Substituting the value of x, we have:

k = 3 / 2

Now, let's consider the question of finding the sum of all possible values of k. Since k can take any value in this case, there are infinitely many possible values. Therefore, the sum of all possible values will also be infinite.

In conclusion, the sum of all possible values of k is infinity.