we know that
if the two rectangles have the same height-to-width ratio
so
height-to-width ratio larger rectangle
21/34---> equation 1
height-to-width ratio smaller rectangle
10/w----> equation 2
equate equation 1 and equation 2
21/34=10/w---------> 21*w=34*10------> w=34*10/21-----> w=16.19
the answer is
w=16.19
