MathNet 2022-part-06 — 196 problems (EN–VI) Question 181

Alice thinks of four positive integers $a \leq b \leq c \leq d$ satisfying $\{ab + cd, ac + bd, ad + bc\} = \{40, 70, 100\}$. What are all the possible tuples $(a, b, c, d)$ that Alice could be thinking of?