There is a slightly more efficient way to find the desired perimeter besides finding each of the side lengths of RSQ.
Since the triangles are similar, every corresponding length is in the same ratio -- this ratio is the scale factor. Thus perimeter ABD:perimeter RSQ = 7:3. It is easy to compute the perimeter of ABD (77), so to find the perimeter of RSQ solve the proportion `77/p=7/3 ` where p is the perimeter of triangle RSQ. This is important to know since the problem could very well have just given you the perimeter of triangle ABD and asked for the perimeter of RSQ.
In this question, triangles ABD and RSQ are similar to each other and similar triangles have a definite proportion of sides.
i.e. AB/RS = BD/SQ = AD/RQ = some ratio (given here as 7/3)
Since we already are given the length of each side of triangle ABD, we can use the above to get the corresponding side lengths for the triangle RSQ (RS, SQ and RQ).
The perimeter of any triangle is the sum of all its sides, which we obtained in previous step.
Since, at enotes, we can not solve the assignment for you, we can only help you to solve it; the above information should be sufficient to enable you.