Question

One square is placed inside another square so that their diagonals overlap. If the larger square has a side of 6 and the smaller square has a side of 4, how far is it from the vertex of the larger square to the corresponding vertex in the smaller square (marked in red)?

2–√

22–√

32–√

4?√

Answer 1

`a_1=4,a_2=6 \\d_1=4 √(2) ,d_2=6 √(2) \\ \\x= (d_2-d_1)/(2)= (6 √(2) -4 √(2))/(2) = (2 √(2) )/(2) = √(2)`