A team-building exercise has teams build a house of cards as high as possible. However, the cards for different teams are of different sizes. Team 1 uses \(10 \mathrm{~cm} \times 10 \mathrm{~cm}\) cards, while Team 2 uses \(8 \mathrm{~cm} \times 8 \mathrm{~cm}\) cards. What is the minimum height when the two teams will be tied? Ignore the width of the cards.