Answer: C

Solution:

Since these triangles are isosceles, we can drop altitudes to create two congruent right triangles as shown in the diagram.

Using the Pythagorean theorem, we get that the altitude of the triangle with area $A$ equals $$\sqrt{25^2 - 15^2} = 20.$$ Similarly, we get that the altitude of the triangle with area $B$ equals $$\sqrt{25^2 - 20^2} = 15.$$

With these altitudes, we can calculate the areas of the triangles. We get that $$A = \dfrac{1}{2} \cdot 20 \cdot 30 = 300.$$ Similarly, $$B = \dfrac{1}{2} \cdot 15 \cdot 40 = 300.$$

Therefore, $A = B.$

Thus, C is the correct answer.