Question

Triangle FGH has the following side lengths: FG = 5 ft, GH = 10 ft, HF = 12 ft Triangle PQR is similar to triangle FGH. The longest side of triangle PQR, RP = 7.2 ft. What are the lengths for the other two sides of triangle PQR?

Answer 1

The first thing we must do for this case is find the scale factor.
 We have then that for the larger side of both triangle, the scale factor is:
 $k = \frac{RP}{HF}$
 $k = \frac{7.2}{12}$
 $k = 0.6$
 To find the other two sides, we must apply the scale factor on each side of the triangle FGH.
 We have then:

 For PQ
 $PQ = k * FG PQ = 0.6 * 5 PQ = 3$

 For QR
 $QR = k * GH QR = 0.6 * 10 QR = 6$

 Answer:
 You have that the lengths for the other two sides of triangle PQR are:
 $PQ = 3 QR = 6$