vanceag2016 wrote:

This question could be phrased better in prompt 1) to read the "least distance from B to the hypotenuse". Personally, I interpreted the use of "height" as a descriptor to imply the distance alongside the perimeter (or one of the sides of the triangle rather than the distance measured within the interior). Hence, I selected E for the answer since we didn't know which side it referred to (8x or 15x).

Hi

In a triangle, the word 'height' means perpendicular from any vertex to the opposite side. So, yes two heights here are already AB and BC. But we should know that AB is height from vertex A to opposite side BC, and BC is the height from vertex C to the opposite side AB. The third height will be from vertex B to the opposite side AC, which is what is constructed here in the diagram by Bunuel.