2011 AMC 8 第 16 题

The two right triangles use legs $15,20,25$ in opposite roles.

Drop an altitude in each isosceles triangle.

Since these triangles are isosceles, the altitude shown from the apex of each triangle bisects its base and creates two congruent right triangles.

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.