Since two sides and one included angle is equal in △PQS and △PRS, we can conclude that they are congruent under the SAS congruence criterion.
Which means :
▪︎Angle S = Angle S
▪︎PS = PS
▪︎QS = RS
Given :
Measure of segment QS = 6n+3
Measure of segment RS = 4n+11
Thus :
[tex] = \tt6n + 3 = 4n + 11[/tex]
[tex] = \tt6n + 3 - 4n = 11[/tex]
[tex] =\tt 2n + 3 = 11[/tex]
[tex] = \tt2n = 11 - 3[/tex]
[tex] = \tt2n = 8[/tex]
[tex] =\tt n = \frac{8}{2} [/tex]
[tex]\hookrightarrow\color{plum}\tt n = 4[/tex]
Thus, the value of n = 4
Measure of segment QS :
[tex] =\tt 6n + 3[/tex]
[tex] = \tt6 \times 4 + 3[/tex]
[tex] = \tt24 + 3[/tex]
[tex]\color{plum}\tt \: \bold{QS = 6n + 3 = \tt\bold{27}}[/tex]
Thus, measure of QS = 27
Measure of RS :
[tex] =\tt 4n + 11[/tex]
[tex] =\tt 4 × 4 + 11 [/tex]
[tex] =\tt 16+11 [/tex]
[tex]\color{plum}\tt \: \bold{RS = 4n + 11 = \tt\bold{27}}[/tex]
Measure of QR :
[tex] =\tt 27+27[/tex]
[tex]\color{plum}\tt \: \bold{QR = 27+27 \tt\bold{=54}}[/tex]
Thus :
▪︎QS = 27
▪︎RS = 27
▪︎QR = 54
Therefore, the correct options are :
▪︎(C) SR = 27
▪︎(D) QR = 54
