hello i was wondering if anybody could help me with the following puzzle i have been trying to solve for a quiz.Thanks

A philosopher and a mathematician meet for the first time in 10 years. Since they last met the philosopher has become a father. He mentions his 3 daughters and the mathematician naturally asks their ages. The philosopher is a bit of a pain, so he says : "The product of their ages (in integer years) is the number of one of the houses we lived in together as students, and the sum of their ages is the number of the other". The mathematician says that he has no chance to solve the puzzle unless the philosopher at least tells him which house is which. The philosopher now says ; "The house number that's the product of my daughters' ages is the one that's a perfect square". The mathematician still can't solve it and is starting to get annoyed, so he asks ; "Which one of your daughters looks most like her mother?". The philosopher is surprised, but he says ; " The eldest, I guess". The mathematician now correctly announces the ages of the philosopher's 3 daughters. Can you?