We are given two similar triangles -- one with sides 5,7, and 10. The other has shortest side 15. We are asked to find the perimeter of the second triangle.
(1) We could find the other two sides of the second triangle. Since the triangles are similar, their sides are in proportion.The scale factor is 5:15 or 1:3 since the shortest sides are corresponding.
Then `1/3=7/x ==> x=21` and `1/3=10/y ==> y=30`
The sides of the second triangle are 15,21,30 and the perimeter is 66.
(2) Another way is to realize that if the triangles are similar, every corresponding linear measurement is in the same proportion -- the scale factor. Thus the lengths of corresponding altitudes are in the same proportion as the lengths of corresponding medians, sides, perimeters, etc...
Since the perimeter of the first triangle is 22 and the scale factor is 1:3 we have `1/3=22/p ==>p=66` as above.