Here it is given that the triangles ABP and DCR are similars, therefore we use the ratio rule which states that
corresponding sides of similar triangles are in same proprtion .
![(AB)/(DC) = (BP)/(CR)](https://img.qammunity.org/2019/formulas/mathematics/high-school/lg1yrs19m0bl1fwmj5vhrwxansf5fy07np.png)
that gives
7/10 = BP/11
7*11=10BP
BP=7.7
Again using the ratio rule
![(AB)/(DC) = (AP)/(DR)](https://img.qammunity.org/2019/formulas/mathematics/high-school/7tit782920pkludvthvsv3fq2bs8wxxt2l.png)
7/10 = AP/6
42 = 10AP
AP = 4.2
Perimeter= AB+BP+AP = 7+7.7+4.2 = 18.9
Correct option is A.